Does anyone know of some easy-to-use "dependency checker" for TL mods? 

That would be fantastic.  Someone with coding skills should write a program to do this!

The DESCRIPTORS here are very different, but rather than having to learn all about them at this point, it should suffice to just notice/look for those DESCRIPTOR blocks which specify a recognizable file-path and file-name...

If you would like to learn more about the DESCRIPTORS specific to particle systems, there's an excellent series of articles here (just look for the "Particles" section) by OedipusRex.

if your concerned about damage, it comes from 4 sources

damage shapes
which are inside layout files that are inside the SKILLS folder, inside there should be a directories that catagorize the skills, eg. the MONSTER folder, but some layouts can be shared by multiple skills

missiles
the MISSILE folder, is its own thing, very easy to spot in the main directory(MEDIA folder)

the skill itself
if you noticed by now skills can come with thier own damage numbers
the two layout types i mentioned above are what deliver the damage, but the values in the skill are what determine it.

affixes
this is whats used to deal flat magical damage, all of them are in the AFFIXES folder.

you can trace all of these back from the skill, although some skills have multiple parts and all of these components can be mixed matched and stacked with each other into varying degrees of complexity.

Hi Nyriox! Oops I only answered your first point...

...I have no idea how to identify all the resources used by any particular skill.  I need to copy all resources (Particles, Units, Sounds, Affixes, etc.) used by all the skills of this particular monster—and I am completely at sea trying to figure out where they all are.

but forgot to answer your more pressing concern!

...the problem I am having is that backported attack skills, when triggered, render their associated monster animations but do not render any particle effects or deal any kind of damage. 

Yes, Twinkle's answer is best. And since you're back-porting, I'll just reiterate the same theme of "making sure the resources are there/present"...

Inside skills, those resources would be...

- any .layouts it's looking for
- any AFFIXES it's looking for (tho Virax's skills seem to all use EFFECTS directly, rather than affixes)

There are more resources a skill can use, but these should be all that are involved for Vyrax's skills. There's a good skills overview article by Chthon on the wiki too.

ill try break down my own process for procuring the right files from a skill, ill use a vyrax skill as an example
ill be leaving out lots of details, since there is so much that the whole thing will be convoluted if i attempt to explain everything.
check out the wiki here if you still haven't
i highly recommend reading up everything from the skills section, the tidbits of information will add up, understanding how skills are made will come with how to find and use files for them.
[SKILL]
<STRING>NAME:Boss_Dragon_Fire_Line
<STRING>ACTIVATION_TYPE:NORMAL
<STRING>TARGET_ALIGNMENT:EVIL
<STRING>ANIMATION:Special_Breath
<FLOAT>RANDOMRANGE:0
<FLOAT>RANGE:20
<BOOL>CAN_PROC_FROM_SKILL:0
<FLOAT>SPEED:0.8
<INTEGER>NUM_PETS_ALLOWED:15
<INTEGER>COOLDOWNMS:7500
<FLOAT>FINDTARGETANGLE:360
<FLOAT>TURNRATEOVERRIDE:-1
<BOOL>CAN_BE_SILENCED:0
<BOOL>ALLOWS_TURNING:0
<BOOL>CAN_APPROACH:0
<INTEGER64>UNIQUE_GUID:5098754330261549009
[EVENT_TRIGGER]
<STRING>FILE:media/skills/monsters/boss_dragon/fire_line.layout
<FLOAT>WEAPONDAMAGEPCT:100
<STRING>DAMAGE_TYPE:FIRE
<BOOL>NOSTRIKEEFFECTS:1
<BOOL>NOSTRIKEPARTICLES:1
<INTEGER>CLONECOUNT:10
[/EVENT_TRIGGER]
[EVENT_TRIGGER]
<STRING>FILE:media/skills/monsters/boss_dragon/fire_line_missiles.layout
<FLOAT>WEAPONDAMAGEPCT:25
<FLOAT>SOAKSCALEPCT:25
<STRING>DAMAGE_TYPE:FIRE
[EFFECTS]
<STRING>TARGET:ENEMY
[EFFECT]
<STRING>ACTIVATION:DYNAMIC
<STRING>DURATION:.5
<STRING>TYPE:KNOCK BACK EFFECT
<FLOAT>FORCE:25
[/EFFECT]
[/EFFECTS]
[/EVENT_TRIGGER]
[EVENT_TRIGGER]
<STRING>FILE:media/skills/monsters/boss_dragon/fire_line_knockback.layout
<FLOAT>WEAPONDAMAGEPCT:1
[EFFECTS]
<STRING>TARGET:ENEMY
[EFFECT]
<STRING>ACTIVATION:DYNAMIC
<STRING>DURATION:.5
<STRING>TYPE:KNOCK BACK EFFECT
<FLOAT>FORCE:25
[/EFFECT]
[/EFFECTS]
[/EVENT_TRIGGER]
[/SKILL]
so heres the code for one of his attacks, its a pretty straight forward one, the layout files are directly referenced in each EVENT_TRIGGER

<STRING>FILE:media/skills/monsters/boss_dragon/fire_line.layout
<STRING>FILE:media/skills/monsters/boss_dragon/fire_line_missiles.layout
<STRING>FILE:media/skills/monsters/boss_dragon/fire_line_knockback.layout

looking at them will tell you where these layout files are
if you click and highlight the EVENT_TRIGGERS a new option appears just bellow the raw code,
that is: Open Layout
this will open the layout that the event uses inside GUTS, so you can see whats inside
typically skills will have:
damage shapes (this determines the area of effect a skill will have)
time lines (this is what triggers everything in the layout files and allows you to fine tune the order of when each component will triggers in the layout)
particle links (which also reference the directory of the particle layout, you will see this under the resource section to the right if you have this component selected to see its properties menu)
sounds (which reference sound files, same as particles, look to the right)
unit spawners (these are used to summon units or spawn missiles, these are referenced by their internal names, typically the internal name will be the same name used for the actual layout file, to see it scroll down the properties menu on the right and look for the resources heading)
missile files are inside the Media/Missiles directory
units files are inside the Media/Units directory
read this tutorial by gyt for a more detailed look into missiles

to look specifically where damage can come from in a skill you should look for these lines, they can be found here in vyraxes skill
      
<FLOAT>WEAPONDAMAGEPCT:X      
<FLOAT>SOAKSCALEPCT:X      
<STRING>DAMAGE_TYPE:FIRE

WEAPONDAMAGEPCT directly controls damage which uses the characters attack stats, this is what i mentioned when i said that the damage can come from the skill itself
SOAKSCALEPCT determines how much of the damage is not considered when caluculated against a targets armor values
at 100% all of the damage will go through armor
DAMAGE_TYPE this determines what kind of damage the skill will do

in the event triggers this also shows up
           [EFFECTS]
         <STRING>TARGET:ENEMY
         [EFFECT]
            <STRING>ACTIVATION:DYNAMIC
            <STRING>DURATION:.5
            <STRING>TYPE:KNOCK BACK EFFECT
            <FLOAT>FORCE:25
         [/EFFECT]
      [/EFFECTS]
i forgot to mention it, but this is also a source of damage, that is, an effect directly attached to an event
functionally these work the same as affixes, since they are what make them up
affixes are just effects that are bulked together and can be further modified, which makes them far more flexible than directly using effects
for this particular skill it doesn't require the extra hassle of making an affix so it just attaches the knock back effect directly to the event

thats about what i would look at to ascertain where all the files are, certain skills can be far more complex, but looking at the vyrax skills i dont think any of them are too complicated, this methodology should work for all of them.

its highly likey that your gonna bump into some compatibility issues, GUTS and TORCHED are for the most part similar but have some differences, im not 100% sure of what they are.