I've had a problem with the game not closing to the desktop from the start. It just fades to a black screen and locks up Explorer so you can't access anything without killing the game in the task manager.
I have a dual-card laptop, and I strongly suspect this is an issue with the video cards not switching from 3D to 2D graphics correctly. The Nvidia software should release the 3D card and the Intel Integrated graphics should take over, but that's not happening as it should.
I suspect this is the issue, because unless the launcher is started in Intel rather than Nvidia graphics, the game crashes on the spinning ship, which I think is the first true 3D object. Again the handover from 2D to 3D seems to be the culprit. I don't know what's happening in the Elite code but it's not handling the graphics cards in the same way as any other 3D game that I own.
I've not found that switching from fullscreen to windowed makes any difference. I've tried deleting all the game files and re-downloading and verifying files and all that. I think this is something intrinsic to the Elite code.
Your issue isn't identical but I tend to agree with the person who suggests there's an issue with the graphics process handing off from 3D to 2D. This isn't likely to be a hardware fault if everything else on your system is running fine, as is the case with mine. If you can run games way more graphically intense than Elite, as I can, the finger of blame points pretty squarely at the Elite software. Still, it's worth borrowing a different graphics card and testing that out; it's the fastest way to prove whether yours has an incompatibility with Elite or not.
I first started submitting tickets for this issue way back in beta, and AFAIK nobody's ever read any of them. I wouldn't hold your breath for tech support, frankly. I've long become resigned to ending the game with ALT-CTRL-DEL (or CTRL-SHIFT-ESC, it's quicker).It doesn't really bother me now, it's just a constant reminder that Elite isn't, well, elite.
BTW I took a brief look around the web for clues, and there are several postings about computers locking up and beeping in some form or another. I didn't find anything exactly as you describe, though, and didn't find any really authoritative solutions. Most answers end up with "re-install Windows", which is a solution but not exactly helpful. Still may be worth you Googling around for "freezes and beeps" or something similar. Good luck!!