|I would test the memory first with Memtest86 from a bootable CD you can prepare.|
Then I would test the hard drive with the hard drive mfg's utility or Seatools from Seagate also from a bootable CD.
IF both test OK then I would perform a Factory restore from either the recovery partition or recovery media if supplied (purchasable from mfg with model and serial number). This would wipe anything off of the system that you might not want including many problems (including infections). After this, update Windows, Drivers, install your preferred antivirus program (or Avast Free version) and set things up the way you like.
Know that many problems could have lead to an incorrect diagnosis of a bad motherboard like a bad power supply, bad memory, a hard drive that was going, an infection or corrupted system file or other hardware problems. Unless you know who and how it was diagnosed, you will either need to wait until problems surface, or begin diagnosing it all over again, which would need symptoms to begin with anyway.
You have to be a little bit crazy to keep you from going insane.