Your talking about the same computer as the one listed here:
http://www.dealtime.com/xPF-E-Machines-eMonster-600-EMONSTER60064 mb of ram, 600mhz P3, 20Gb HDD?
and you are trying to install windows 7 on it??? Yikes!
Thats well below minimum requirements:
http://windows.microsoft.com/systemrequirementsbut it's worth a shot, so first off how did you eliminate all the idiot factors (we all do it from time to time) are you sure your booting through a DVD Rom and not a CD Rom drive? they are often not labeled, I've made that mistake before. And it sounds like you have thoroughly tested the disks themselves.
I think you have a bigger problem, flashing the BIOS with a custom BIOS could have messed something up, or there might be an issue with an older motherboard being able to boot from a DVD drive or even a CD drive, since this computer is a dinosaur it came with windows 98 which required you to boot from a floppy first and then insert the Win 98 CD if I remember right.
My guess is that it's not a windows 7 issue since you would have to load windows setup to get any hardware errors. And as far as minimum requirements go... I recently successfully installed win 7 on a P4 w/756mb of ram, slightly below the 1GB min.
It's probably the motherboard or BIOS if the DVD drive and Hard Drive are ok. Go in your BIOS and see if there is an option to boot from USB, make sure it's enabled and select "Removable Device" as your primary boot device, Then you are able to boot off a USB Hard Drive... Just place a Win 7 Image File in the root folder of the USB Hard Drive and cross your fingers.
If that doesn't work, I would call it quites. The computer is just too old for the goodness of Win 7, time to upgrade if your machine is more than 10 years old.