Crashing/slow after installling video drivers, beeping inside case

Recently started having an issue where once windows login screen comes up I can hear beeping coming from my case. Then once I try to login I can hear hard drive try to spin up and system will freeze every time I hear hard drive spin up (every 5-15 seconds) during login. Sometimes this persists, sometimes it goes away within a few minutes and the system runs fine but I can still hear beeping from inside the case. Other times I get either a complete lockup, a BSOD, or the computer restarts itself without any warning.

I don't have any of these issues until I install graphics drivers.

-I've tried testing memory in windows memory diagnostics w/ 4 passes it came back w/ no errors.
-I tried a clean install which runs fine until I install graphics drivers(I've tried multiple different versions all have the same issue)
-I tried installing a new hard drive but am still having the same issues.

I've tried to listen where the beeping is coming from but I'm having a hard time isolating it. It's fairly short, rapid and somewhat faint.

Hardware specs are:

Western Digital WD Black WD1001FALS 1TB 7200 RPM SATA 3.0Gb/s 3.5" Internal Hard Drive
G.SKILL 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1600
CORSAIR CMPSU-750TX 750W ATX12V v2.2
Intel Core i5-750 Lynnfield 2.66GHz LGA 1156 95W Quad-Core Processor
MSI R5770 Hawk Radeon HD 5770 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card
GIGABYTE GA-P55A-UD4P LGA 1156 Intel P55 SATA 6Gb/s USB 3.0 ATX Intel Motherboard w/ USB 3.0 & SATA 6 Gb/s

I really have no idea what might be causing this an would appreciate any advice, Thank you

Ty for the reply
I have tried two different sets of drivers for my card from the ATI/AMD website for my version of windows (7 ultimate x64), the most recent 12.10 and a few versions back 12.4. Same issue with both. Also tried the one from windows update, still same issue

Right now the computer is running "fine"(still intermittent "beeping"), but I'm afraid to restart it.

Have you ever attempted to overclock this card?

I have never tried overclocking it.

Have you made any custom changes in the BIOS settings?

I've tried using the optimized settings and fail-safe setting in bios neither seem to have an effect. Other than that I haven't changed anything.

Have you checked with AMD to see if there is a firmware update for the card?

I think there might be a more recent version for the firmware but I will have to double check once I get home. Will post a reply after I try updating.

Is the card still under warranty?

Card is still under warranty for parts but not for labor.

What does it look like in the device manager? Do you have the 6 pin power cable connected to the card?