Well, from what information you have, here's my way of thinking.
There are four ways to do that car:
A: Put valet key in a universal bypass module and hardwire all connections, including running wire(s) for factory alarm disarm (and maybe arm too) into the driver's door. (Customer loses valet key.)
B: Buy an (expensive-ish) all-in-one module that handles transponder bypass, and controls car's doorlocks and other convenience features through data, saving the time/labor of running wires into the door. (Customer keeps all keys.)
C: Buy a no-key-required bypass module, but still hardwire all other connections, including arm/disarm in door. (Customer keeps all keys.)
D: Buy two separate modules: One for transponder, one for doorlocks. (Customer keeps all keys.)
My opinion:
---Back in 2005 when this car was new, we didn't have Option B because those all-in-one modules didn't exist yet.
---Your finding of wires fished into the driver's door rules out Options B and D, and leaves us only with A and C as possiblities.
---This car has a black "hush panel" under the driver's dash, above where the driver's feet would go. You can't see much of anything without a little disassembly. You probably won't be able to tell if the previous installer used A or C, and whether or not they left any product (spare key, bypass module, et cetera) behind.
---If/when you do finally get the car apart, look at the car's key cylinder for clues. If they did A, there will be a "ring" around the car's keyhole, leading to a black box with the valet key inside. (Do a google image search for "556U" for an example.) If they did C, you should see splices made to the thin wires coming from the factory immobilizer module around the key cylinder.
WHAT I WOULD DO IF I WERE YOU:
1. Have your daughter look for a remote-start antenna on the windshield. If the antenna is still there, you might get lucky and even have a complete system already installed; you'd just have to hunt for remotes to buy.
2. If there's no antenna there or you can't be sure what's in the car.....hmm. Well, you'd hate to buy parts only to find out there's something already in the car. On the other hand, it'd suck if you got there to do the install and didn't have what you need.
3. Maybe you could go there with the new Viper and your tools, and scout out ahead of time a shop local to the car that will sell you an all-in-one bypass module if you need it.
4. If you go to Best Buy (or any other shop), you'll find that most shops wouldn't even want to re-use any of the stuff that might be in there. They'll understandably want to sell you everything new, so they'll be able to guarantee the job. You might find a small local place willing to re-use the bypass if you shop around enough.
5. So anyway, I know you said you're on a limited budget, but also, how much is your time worth to you? Plus, if you're doing this yourself, you're saving so much money that a few bucks here or there for parts hopefully shouldn't be too bad.
If you want to go there in one trip and be 100% sure of getting the car done the first time, maybe just shell out for an all-in-one bypass from ADS (idatalink.com) or Fortin (ifar.ca).
If you take the car apart and find a box with a valet key inside, consider it a bonus that she now has a spare key.