Hi!
At this point you don't have a really good way to see if you're having a hardware or software problem. As this is a refurb. you just can't trust the hardware, it's the nature of the beast. That being said, both newegg.com and tigerdirect.com have USB - wireless adapters available for about $20. You may want to consider getting one of those as a baseline. Disable your built in wireless and install the new adapter. You can reasonably assume the new device works, so if the problem persists, you can narrow your troubleshooting down to the software (OS) / driver arena. OTOH, disabling the problematic device and installing a (presumed) good one may just fix the problem entirely.
Good luck!