Wowexec.exe is part of Windows XPs 16bit subsystem.
It is a sort of DOS/16-bit emulation which allows the running of older pre XP programs.
When you see it in Task Manager it does indeed show no resource usage.
It certainly isn't a virus click here
Perhaps you could explain your actual problem in detail and give us your system specs.
The fact you are seeing wowexec in Task manager suggests you have a old/DOS program running on your system.Do you know of any old prgrams that you have on the pc?
Have you checked with any anti-virus/anti-spyware scanners that your system is clean?