If you have access to an older AGP card, try that in there and see if boots up.
Boot the PC with the case off and visually check if all the fans spin.
Do you get any BIOS beeps at all ??
You might, possibly, be on the right track with the power supply output. Although 250w should be fine, you may need a little more. When you switch your PC on there might be such a draw of power that it is too much for your PSU (remember 80% efficiency is probably what you get). This would result in not very much happening other than fans spinning, and HDD powering up. If this is the case, then your motherboard should limit start-up to just the accessories. Although not overly common on PC's, it is a possibility.
It could also be that the card is not functioning. When you say you get no signal, do you mean your monitor is telling you this (as I presume it will), or that it is just blank.
Check your motherboard's BIOS for settings. Also check if BIOS updates are available.
Your card could well be damaged, or simply non-functional. Personally, as it's brand new, I would just swap it for a new one!
Also if you have have a RAM upgrade, try removing the newer one. Sometimes the timings on certain RAM chips can cause issues with AGP, again rare, but possible.
If you get no BIOS beeps though, I would imagine that it's a power problem.
The initialization sequence is > motherboard & devices get power 1> AGP/VGA initialzes 2> BIOS loads to memory 3> BIOS test 4> Boot sequence.
Your BIOS should beep at stage 2, so if you don't get this beep, it's probably power. If the card is 'dead' then you get multiple BIOS beeps. If the card's output connector is bad, then it will load as usual, only you wonn't see anything, but you will hear normal noises.
Hope this helps.