If it's on an Intel Chip Set M'Board there should be no Chip Set Compatibility problems but the VIA and SIS may be a different story.
The 9600 ATI cards have been very reliable in my experience but then again I've only ever used 2 different brands of them ABit & Expert Vision brands. I've yet to have one go bad but it could very well be your Power Supply being over taxed and killing off the Video.
If you can try the Video Card in a different computer to see if it's actually working properly, if you don't have another computer around with that Format Video Card I would try a different Power Supply depending on where you are an Antec would be my first choice but there are other good brands out there but get one with at least 450W capacity and the Antec Smart Power ones are very good even if the back fan doesn't ever spin as the power supply never gets hot enough to require the extra cooling.
Make sure that all the power plugs into the M'Board are actually plugged in and any that go to the Video Card if there is one. Generally there are 3 power connectors on a P4 M'Board the normal 20/24 Pin main one a secondary 4/6 pin one and then a third one often over looked a normal 4 pin HDD type connector this one quite often gets forgotten about if there is one there and places extra load on the M'Board to distribute the available power around to where it's needed.
If your current Video Card is in the process of dieing you don't want to fit another one as you are only treating a symptom and not coming up with a cure.
It's also possible that the Video Card just overheated if that's the case you need to make more air flow through the case.