Look at the tables at:
http://www.pchell.com/hardware/beepcodes.shtmlFor example,
AMD BIOS would be 8 short beeps for a bad display adapter.
Phoenix would be 3 (pause) 4 (pause) for a bad display adapter
There are other sequences depending on which BIOS you have. If you run a Google search on "bios beep codes", you'll find a bunch of such sites.
The trick is to listen carefully - it might be something else including the motherboard. It would help if you already knew what kind of BIOS you have. That's the first thing that shows up on your machine when you boot unless your graphics card presents its bios info first (which is often the case). The graphics card bios information usually goes away quickly and then the boot begins with the BIOS type and version. Obviously you can't see that now, but pick your brain to see if you can remember which one it was.
I had one fail a few years ago and was pissed that I couldn't find any card in any retail store for less than $100. I got one on eBay for $17 including delivery - the guy selling it was a gamer and a new $300 card had just come out with twice as much memory so he upgraded and wanted to unload the old one. It was better than the card I was replacing! Apparently that's a common reason why you can get great graphics cards for very little on eBay.