Welcome to the Forum,

Try the Dell Diagnostic Floppy Disks.

If you don't have them, they can be downloaded from your Product Support
accessed under Notebooks^ at top left of this page.

Thanks - I tried the diagnostics and it won't boot of the floppy (or anything for that matter).  I tried it with and without the hard drive installed.

LINK HERE for How do I troubleshoot a system that will not start?

Quote from above site:

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# Remove the battery, hard drive, CD/floppy drive, and any PCMCIA card. Remove any external peripheral components such as printers, palmtop devices,
or USB devices. Remove the RAM, this should cause the system to power on and off in a cycle. If not, reinsert the RAM and check the BIOS. Will the system POST?

# Install one memory module, and attempt to boot. Install the second module if the system does boot. If the system does not POST, use the same module in the 2nd slot.
If the system completes POST, replace the motherboard for a bad RAM slot. If the system does not POST, remove the memory module and place the other module in this slot.
If the system completes POST, replace the memory for a bad DIMM. Otherwise, replace motherboard.