If the PC is powering on and running the software, there's little reason to blame the maker of the system. In this case, you should do the usual things, run a full malware sweep and antivirus scan first. Malware Bytes / SUPERAntiSpyware make a great one-two punch for initial scans, and then I'd suggest running an AV scanner like Avira or Microsoft Security Essentials to pick up anything else.
If those come back clean, it's possible that there's software that might be the root cause, in which case, a system reload may not be a bad idea. It's worth noting however that Windows often spawns multiple copies of explorer.exe depending on what you're doing. One instance by itself with no windows open is usually just the explorer shell, and any subsequent processes are open file explorer processes. Confusing enough. Firefox will spawn multiple processes only in rare situations, multiple copies of it aren't common. Chrome on the other hand spawns threads like children spawn germs.