It sounds ore like a hardware issue than a virus/ mallware issue.

Try changing your CMOS battery on your motherboard and take out your memory then put it back in again. If this don't help then scan your hard drive within windows (you'll probably have to schedule it to do this task when windows restarts).

With the problems you mentioned about DVD's taking ages to burn, random beeps , the clock and usb devices not being recognised sounds like a motherboard problem. Try starting windows in safe model to see if these problems go away. If they do then you can bet its a windows/driver problem. If all this fails then before reinstalling try system restore to an earlier point before these problems started happening to try and fix this.