Hmm indeed!
1) I don't want to exclude a hardware error, though i find it very much unlikely. I tried three different sets of fresh, non-rechargeable batteries. I also reformatted the player a couple of times already.
2) I triple-checked the MTP drivers, uninstalled them, erased every trace of them from the registry, reinstalled them to no avail. And did the whole thing over again. Same problems as before.
3) You can never be too careful when it comes to Windows, even 2k, but I'm pretty sure everything is functioning properly. I use Win2k Pro SP4 with proper patches (post-sp4 patch rollup), and I keep doing regular maintenance on my system. I haven't done a complete Win2k reinstall for quite some time, and I'm not very keen on it. Especially regarding the lots of different applications I have installed for many different purposes. Which might actually be exactly the problem.
I have a feeling that there might be some kind of cross-incompatibility with other software here, which is hard to track down.
Now, maybe I have a problem with Mediamonkey? What leads me to that conclusion is the fact that MM is not able to write proper filenames on the T30. I can copy .mp3 files alright with WMP9 (up to the point where the connection freezes, just like Taucher writes in
this thread).
The files copied with WMP9 have proper filenames+filetype extensions. BUT if I copy any kind of file with MM, I just get unusable files on my T30 (the size roughly equals the filesize on my PC's HDD), named '.MP3', '.TXT', and most annoying, '.HEX'.
Maybe there is some other software capable of sending data files to the player like Mediamonkey? I haven't found any yet, but maybe there is?
I might try at some friends PC, but I'm beginning to think if the fuss is worth it. I might as well get another player from a different company. But somehow I can't let go off this problem, and I want to find a solution by all means.
So, I don't expect you to solve this for me magically, and I'm really thankful for your responses. Thanks for that.

I will try around a little more and maybe return the player to the store next week.