Based on the symptoms it looks to be a video card problem. The 2 beeps mean video errors, in this case the PCI Express slot is detecting problem on the video card:
Please check the following link for detail information: page 67 table 37 “BIOS Beep Codes”
Also as you can hear the Windows boot up sound normally, but not video.
Now in regards the system booting up on safe mode, is because the video requirements in that mode are lower than the normal mode. I suggest trying other video card, to narrow the problem on the video card.