The problem with malware these days is that they duplicate, inherit and copy themselves around. The "new" malware usually remains undetected for days, if not weeks or even months.
Your computer gets infected -> your computer will stay infected, this in most cases. Anti-virus software these days is becoming obsolete day by day. Either reinstall Windows or run the scans daily, try to keep open programs to bare minimum and hope for the best.
The best solution would be to install security-wise decent operating system.
Edit: Actually RAM gets wiped when the computer shuts down. However, upon the boot all the cells will be wiped once again to make sure everything is clean. Malware which infects BIOS/firmware are VERY limited. Usually they can only do one task, which is surprise surprise, shut down the machine, reboot it or something as simple. This however depends on the spare space they have to play around with.
Practically there is no way to infect the BIOS and cause serious harm. I am aware of known exploits which have done this however, but these days they are extremely rare, thanks to more caution and security by BIOS manufacturers. Also infecting MBR isn't that practical either, yet still possible.
