could this be sings of the dreaded motherboard failure?
I'll defer somewhat to JackMDS, since he recommends an obvious first step.
However. That's an LGA-775 Gigabyte motherboard. We built two Gigabyte systems with a similar model -- wait a minute -- three -- the third one was full ATX P45. Or EP45. Doesn't matter. All of those boards died after six to eight years -- the last one failed two months ago.
Maybe Jack would concur with this. After you've tested for malware infection, get something like HCI Memtest 64 downloaded on a different computer with ISO burned to CD or to USB following the instructions. Run that self-bootable CD on the subject LGA-775 system. If there are failures with RAM, it could still mean any of several things, including a motherboard or PSU gone south.
Troubleshooting is a sort of masochistic activity that I pursue feverishly to a point. But it is a matter of costs and benefits -- in time, in sweat, in trouble, and in dollars. I will only say that the Gigabyte system that died two months ago did not get much in that sort of attention. We "harvested" the Intel SSD, processor and RAM, and sent the motherboard, PSU and case to the county electronic recycler. My friend in Virginia will get the processor and RAM, and he knows they may be good, and then again not. I wouldn't even ask him for postage in that situation.