Probably it won't help you much, but something similar (but not quite) happened to me some time ago.
I had a good ol' (and that has always worked) PC with a Via Epia board (one of those mini-Itx ones).
After a huge storm, with blackout and n times power going out and coming back, the thingy that ran Windows 2000 just fine started BSODing without a real reason (but it worked in DOS alright).
At the time it was a spare-spare machine so I did not put much importance to the issue, and when I happened to find a similar board on e-bay for a few bucks, replaced the board.
The machine with the new motherboard worked alright (I tested it with a CRT monitor), and set it back as spare-spare/for random tests only.
When it came the time to put into service (still with the CRT monitor) it worked alright.
At a given point I was gifted with one of those el-cheapo 16" (of a never heard before make/model) LCD TV's (that are mainly TV's but that do have a VGA input) and I decided to replace the CRT with it.
Problem: I could not anymore access the BIOS setup (the LCD TV could not "hook" the video signal) but once Windows 2000 booted, it was fine.
Tested again with the CRT, no issues whatsoever.
I concluded that the stupid LCD TV was "below standard" for *some* reasons.
It was a PITA, but since you don't really have to enter BIOS every day, I was fine with swapping the LCD with a CRT in th erare case I had to change something in BIOS setup.
The machine worked fine and was connected through the network to a printer, and had no issues whatsoever.
Once I needed to test a good ol' HP 1100 connecting it directly to the parallel port.
Everything started to act "queer", in Device Manager a "phantom" Parallel port and a "phantom" Serial appeared, IRQ assigning got garbled, etc.
Without the printer (which worked fine on another PC connected) everything was fine.
Out of cannot say what kind of inspiration (or desperation) I replaced the PSU, and suddenly the printer started working alright, IRQ's were fine, no "phantom" devices, everything OK.
The surprise came when I tried again to access the BIOS with the LCD TV connected, and it also worked fine!
I had blamed wrongly the good Chinese guys who manufactured the el-cheapo TV!
The only logical explanation in my case was that *some* defect in the PSU *somehow* introduced some sort of *queer* frequence, and that *somehow* once the 2K drivers set the video to a higher resolution rate disappeared.
I thought that it was one of those extremely rare cases that only Murphy's Law could actually explain, but your issue seems to have some common points with it.
Safe mode should be the same "standard" video output as the BIOS setup page.
Does this latter work for you?