For the benefit of anyone who suffers the same outcomes I have, below are the step I undertook to revive my computer from a 'dead like' state.
On the advice of a local computer store tech, I...
1) completely disconnected all the drives (floppy, cd-rom, hard drive) from the motherboard (i.e. pulled out the power cords and cables connecting them to the motherboard)
2) removed all other peripherals from the motherboard (i.e. took out all PCI, AGP, etc. cards)
3) left only the keyboard and monitor connected, then rebooted the PC.
Compare to the previous boots where only the light on the CD-ROM flashed once, I was now getting a few different beeps (one of which continued non-stop). Video wasn't working, but at least I had more life in the computer than before.
4) Next I turned off the PC, reconnected the floppy drive, put in my bootable floppy disk, and turned the PC back on.
The beeping noises disappeared, and I could here the PC booting, but still no video to see what was going on.
5) Next I powered off the PC, placed an AGP video card in the AGP slot, and turned the PC back on.
As luck would have it, video came through and I was able to see the PC was booting nicely to a DOS prompt off the floppy. I immediately ran the flash utility and reinstalled my old bios.
6) Next I powered off the PC, replaced all my peripherals and reconnected all my drives.
When I turned the PC back on, the computer instantly returned to working order, and if nothing ever happened. I’m still without the 1440x900 resolution option I was originally after, but at least my PC is working again.
If anyone believes they no why the patched bios didn’t work for my motherboard, I may be willing to try another bios upgrade in the future.
Thanks to everyone who responded on the thread.