As far as I know the only way to connect to your iPod via wifi is using SSH, which requires a jailbroken iPod and then OpenSSH to have been installed. This allows you to transfer files and execute commands such as reboot etc but I don't think a restore would be possible as it is a fairly slow protocol, and it needs to be connected through iTunes via USB for a restore. Jailbreaking itself requires a USB connection, so you can't do that anyway- assuming you are on OS 2.x or 3.x.
However I can't see how you got to this state, as I doubt filling up the memory completely would cause this, as you can't access the system partition of the disk without jailbreaking, therefore leaving space for system functions. How are you still receiving push notifications? Does it reach the home screen or get stuck on the connect to iTunes screen?
Are you sure the problem is not the USB cable? Mine is starting to deteriorate after over 1 year's use already- may be it is worth trying another cable. Does the PC recognise that it is connected? Does the iPod charge from the PC?