Can a computer virus control your computer?

Yes, if you let it. A virus is, by definition, a program that duplicates itself, spreading itself throughout a network, possibly mutating itself to avoid detection, just like a real-life virus. However it's the payload that does the actual damage, and that could do anything or nothing at all, and everything in between. Even if your anti-virus misses the virus, it should still be on the lookout for malicious activity, as should your firewall (and even the CPU itself!). Even with these safeguards, never permit anything onto your computer unless the source is validated. A legitimate executable will always advertise its source so if in doubt, take it out. But always check online for advice, as there are often exceptions (false positives).