Perhaps it's time we all took a step back and review what we know from what we've been told:
Dell Inspiron 1100. XP
Stop Error.
Can access the BIOS by F2, but not Diagnostics or Boot Menu
Accessing the BIOS is information only, no fields changeable.
Can boot to Safe Mode, but Video is incomplete and CMD window size (sounds more like Boot to Safe Mode, Command Prompt... not normal full screen Safe Mode)
Memory swapped out, not tested.
Cannot boot to CD
Command Console was loaded. Chkdsk runs ok.
Access Denied when changing settings in MSCONFIG
Owner wants files backed up
Insufficient power at USB port to run (assuming) un-powered external HDD provided by owner.
AC Adapter may not be original or is defective
Maybe more... I forget.
Unknowns: Was the laptop part of a Domain, with policies applied? Was there a setup password applied in BIOS, and were options to boot to diagnostics and boot menu disabled in BIOS?
Thoughts and observations: A lot of time has been spent by the OP and by members of this forum trying to figure this baby out... with no success so far. Nothing the OP has tried, and nothing any of us have suggested have been tried or if tried, produced positive results.
I don't know how much more time and effort you want to put into this machine, but here are some suggestions:
If the boot options have been disabled in BIOS, and a setup password applied, unknown whether a Nuke & Pave would even work, since that would require booting from the CD, which reportedly does not work.
To satisfy the owner's request, recommend pulling the hard drive, slave to another computer (with a 2.5" IDE adapter) or external 2.5" USB caddy and make the backups.
Ask the owner if he has any knowledge of a BIOS password being set. Clearing the BIOS on the 1100 requires unsoldering the CMOS battery. Check the Dell support site to see if there's an updated BIOS for your machine.
See if you can find another working Dell 90W AC Adapter. If you still get the error message, this could be an indication of motherboard fault.
Or, if the BIOS cannot be fixed, and nothing else seems to work, swap out the motherboard yourself or ship the entire unit to one of us or a commercial laptop repair facility. USACVLR specializes in laptops, you might ask him if he wants to take it on.