The only information I could find on installing the update is that in the readme which simply says to follow the steps in the updater, which I did, putting all of the files in the Worms folder.
That said, I believe that the update is installed correctly; however, whenever I try to start a game of any kind it crashes as though the game were not updated at all.

Is there something I'm missing concerning the installation of the update and are there possibly steps that I haven't taken? I've also checked that my drivers are up to date since I 've recently reinstalled XP.

Also I should note that I'm not using any video card that would cause a problem.

You said you "put all of the files in the Worms folder", that makes me think you've installed the wrong thing. The installer is a self extracting exe file that will take care of everything for you. If you're not sure if you have the right file, make sure it's the same as this one (http://worms.thecybershadow.net/files/WA_update-3.6.28.0_Beta_Installer.exe)

Yes, that's the same file that I've used, so I'm quite baffled as to why it didn't seem to work. The disc I have is the Sold Out version, if that's going to cause an issue (though I'm under the impression that with this beta it doesn't matter).

Is an ERRORLOG.TXT file created when W:A crashes?

Where would I find that? Sorry, I'm technologically illiterate.

in the exact same folder the game was installed to.

Nope, can't say I see anything like that.

Ok, what is the information in the "Error signature" section in the dialog when you press the "click here" link in the error dialog?
It looks similar to this:
AppName: crash.exe AppVer: 0.0.0.0 ModName: crash.exe
ModVer: 0.0.0.0 Offset: 00001243
You can copy it to your clipboard by selecting it and pressing Ctrl+C.

OK, here's what I'm getting:

AppName: wa.exe AppVer: 3.6.28.0 ModName: ntdll.dll
ModVer: 5.1.2600.2180 Offset: 00010e03

Thanks for the help so far. I'm going to feel really lame if I'm just making a stupid mistake or if this is something that has been covered dozens of times, but I can't seem to figure anything out on my own.

EDIT: I also got an errorlog file this time. Anything you need to know from that?

Yes, please compress and upload it.

I believe, sir, that this is the file you are looking for.

We have no ready solution for the type of errors like in the error log you've submitted (it's a memory corruption issue of an yet unknown cause). But it seems that you have at least something working. It is "normal" for the game to crash time to time due to a few known issues, but this shouldn't impact the game's playability on a larger scale. Thus, unless you get such errors so often (or always) that it makes the game unplayable, there's no reason for worries.