iMac keeps beeping continuously at random (2010 Yosemite 10.10.2)

Hi,

This problem has been persisting for a few months now. My iMac will randomly start beeping (like a key is stuck) in rapid fashion. The cursor will also occasionally have trouble navigating to other menu options in whatever program I'm in. I usually have to either close whatever program I'm in, open a new program, or restart to get it to stop.

I uninstalled Java, hoping that was issue but no luck. I rebooted in safe mode and didn't hear anything which makes me think it's software related, but I haven't been able to isolate what's causing it. I've scanned the Activity Monitor but nothing jumped out as being off (although I'm not sure what exactly to look for anyway). I wanted to run a Hardware Test but the test screen wouldn't come up when holding D or Option+D. I also don't have the install disks to run the Hardware test either. I've tried to look at it newly installed programs which could have caused it, uninstalled a few, but the issue still remains.

Looking for some help here as I'm about at my wit's end with this. My iMac is from mid-2010 and runs Yosemite 10.10.2 with 4GBs of RAM. I haven't tried to do any hardware upgrades on it or anything.

Thanks!