Two things, and one of them is right there in your post. (500w generic)
One, make sure the card is seated and that you have the lock engaged. If there is a six pin power connector on the card, make sure it's connected to the correct PCI power cable from the PSU. Cards that require power from the PSU rather than the motherboard will not operate without this connection and many generic PSUs lack the proper connectors as they are intended for very cheap systems that do not have PCIe cards.
Two, and the more likely of the two, the generic power supply is not capable of providing the standard ATX specification power. Cheap PSUs are the number one issue with hardware problems and failures. Regardless that it worked with a lower end card that didn't need the full 75w or more of power, the bigger card may not be getting the power it needs. In any case, a generic PSU is not recommended for use with any gaming system for any reason. I recommend you acquire at least a Tier 3 PSU of 450w or greater with a model number that matches one listed on the tier list below. Do not get a generic or off brand unit as you will put your system at risk and likely just have the same issues you have now. If you can get one, an Antec VP-450 would be a good choice that's relatively inexpensive, but there are many others as well.
PSU Tier list:http://www.tomshardware.com/forum/id-1804779/power-supply-unit-tier-list.html