I am assuming by "data page" you mean the POST screen? What is the last thing it writes out prior to hanging?
Try cleaning the PC of any dust buildup and reseat all components (cards, memory, cpu, etc). I have seen similar problems where this did the trick....
You may also want to check your boot order in the BIOS setup and have floppy before the HDD. On your cold boots have a bootable DOS disk inserted and see if it boots. Ok, I tend to doubt this will make a difference bcause I think you'd prob be getting an "OS not found" message of some sort before it hung...
Really the only other thing I can think of is stripping down the PC to a minimal configuration and swapping components, and that's gonna be a painfully slow process in your situation. Intermittant problems that only occur like on a cold start can be very annoying.
edit: some typos fixed 