Hello Sharon,
What kind of VPN are you using? Cisco IPSec VPN Client or AnyConnect?
When you connect using the Wireless, can you see the traffic being encrypted on the VPN Client (check this under statistics)?
Use a Packet Capture software like (Wireshark) to confirm what are the packets doing and if you can see the packets going through the VPN or no.
What you need to confirm first is if the packets are being encrypted or no. If not, so the problem is your Wireless Adapter. And at this point it looks like because using the same PC and wired connection the same VPN Software works. At the end, you tried uninstall/reinstall the Wireless Drivers, and I will say reimage the PC will be the easiest option to figure it out the problem.