The TiVo only has a 50MHz RISC processor, and very limited memory. Some of your hacks do not sound conducive with letting it do the job that it was intended to do. Were any of the MP3 player, games(!) and streaming video server running at the time?
I would definitely consider replacing your PSU, since they do wear out.
All those symptoms point to a PSU going down. I speak from experience as I just changed the HD on my TiVo and still got everything you are seeing. I found when forcing a daily call it caused a reboot suggesting initialising the modem (or cachecard) was increasing power requirements.
I have installed the new disk with the fresh image and its workin well, really fast in the menu's. I think the problems were down to the tivo running too much in the background, or badly configured setup by me, lol.
Anyway Im glad that I was forced to re-image a drive coz now i know how easy it is!
Series 1 Tivo with 120GB HD, Trust 400VA UPS. Tivoweb, TivoNet, External Streaming Video - spare pc!