You motherboard is good. Or mostly good.
Can you do this?
Place Video card in the right slot.
Disconnect the CD ROM. (To save power.)
Plug monitor into the output of the video card.
Make sure card is in place. poser up and try to get into the BIOS.
If you can get into the BIOS with the new Video card, you are mostly good.
Yes, a 300 watt supply is on the low side for many graphics cards.
What is the rated power consumption of your new card?
Some Graphics cards may need about 90 watts. Your Motherboard and CPU and fan might require about 60 watts, give or take. Each drive about 20 watts. GB memory stick about 10 watts each, but this can vary a whole lot. Keyboard and mouse almost nothing. Maybe 5 watts. It would seem that 300 Watts would work, but if any component in your system is drawing more current that it should, you could hit the 300 watt limit. Also, power supplies are often rated with room temp of 70 F and free air flow. Which is not like the inside of your box The temp in the box can rise to 80F and air flow cut in half by cables and confined space.
Now then, after after saying that, I still do not think it was the powers supply itself. It is very possible the Graphics card was bad out of the box. If you really were card full and followed instructions it should have worked. The card does not draw a lot of power until you get into fast 3-D action, like a game.
I just assumed you did not flow instructions just because I seldom do.