Well it's not necessarily the video card. Just because it powers up with no video doesn't automatically mean it's the card.
If your computer isn't POST'ing then it could be the CPU, Mobo, memory OR video card.
The only way to find out is to remove the video card, if the system BEEPS then try reseating the card in there again. If you boot up the system and it does nothing then chances are it IS the card in that situation but you gotta make sure that the system beeps when you pull the card out so you know for sure that the no video is being caused by that.
If not, then you pull out the RAM and see if the computer beeps, if it does and you reseat the RAM and then it does nothing, chances are it's the RAM.
Also though, yeah a 250w PSU is REALLY weak, but you don't have an insane power house running but still I'd recommend 350 or so with a good +12v rail of 16-18a for a smaller system