Is this a reparable problem
Generally, virtually all of broken computer problems are repairable, the right question is how much time, money, and other resources it will take to enact the repairs, and whether the benefits of the repaired computer worth the cost. If all you need is to pull some data - you're better off simply pulling the drive out of the machine, putting it into enclosure/dock and connecting it to a working machine.
and what might be the cause?
Is the red light that comes on supposed to be a power-on indicator? I assume the machine makes no noise of any sort? See the comment by @supercat - one of the possibilities is indeed electrolytic capacitor failure. I also have a couple of a bit older ThinkPads that similarly don't turn on, except IIRC in their case no light comes on at all, and the culprit is faulty DC-DC converters. Those are harder to replace, but not impossible either. The main trick is figuring out which component(s) is(are) faulty, and I'm afraid I don't know enough about hardware to provide a some kind of universal guide as an answer.
If I can't get the machine to boot is it possible to take out the drive, put it in an enclosure, and access the files that way?
Absolutely. The drives used in those machines are likely older 2.5" IDE drives, so you'll need an appropriate adapter/enclosure. IDE adapter would be different from more modern SATA, and you'll need one designed specifically for 2.5" IDE drives as it is different from 3.5" IDE connector - 3.5" IDE has 40 pins and a separate power connector, whereas 2.5" IDE uses 44-pin connector with smaller pitch that also provides power to the drive. I like this one from Yootop for portability, but you might want to get something like this universal Unitek adapter for a bit more future-proofing.
Could I put the drive in an enclosure and link it to a more recent computer (say a Dell) and run it from there, bypassing the PW?
Most likely - AFAIK until Vista Windows did not provide built-in full-disk encryption (though NTFS did support encrypted files/directories since Windows 2000 - feature called Encrypting File System or EFS), so unless someone ever encrypted some files using EFS or used third-party tools like TrueCrypt you should be able to connect the drive to virtually any modern system, be it a Windows, Linux, macOS, BSD, or even a Haiku machine and get the data off the drive. In fact, there are even some tools that may allow you to reset the user passwords in the OS on the drive, should you wish to attempt the repairs on the machine and put the drive back in. And no, unless the drive is encrypted (in which case you'll need to have the password or other key required to decrypt it) you won't ever need to know the original administrator password on that machine to access any unencrypted files on that drive.