I had this happen on a system. Not an XPS, but an Optiplex. Turned out it was the CPU in the end. Not before I replaced the motherboard 2X and RAM 2X because I kept getting contradictory diagnostic codes.

However, I have also had systems (I fix Dell systems for a living) where a solid amber power LED meant the motherboard went bad.

In either case, unless the system is under warranty, it's probably not worth the expense of fixing. And the odds of a P4 system still being under warranty seems pretty slim.

You can troll ebay listings looking for parts, and there's also a place I use when I need to do an out of warranty repair called www.used-pcs.com. Just call them up, tell them what you need, and they'll tell you if they have any, what it costs, etc.