Did they say anything? Or what did they try to troubleshoot?
Have you tried sending your service books? Take a look here: KB15402-How to send service books using the email setup application on the BlackBerry smartphone
Also, have you tried another wifi network? And have you deleted and then re-added any of your wifi network?
If you can, let's see the screenshot of your main home screen, with wifi on.
This is a very common problem with the Blackberry's. They tend to hang and sometimes do not respond to the wifi network. I was having the same problem until when i got some advice from my little brother. I tell you guys he is a complete gadget freak. He suggested me to format the phone or better set to factory settings. i did it and yeah..the problem was actually resolved. I advice you to do the same but don't forget to backup your data.
First of all Active your wifi than follow these simple steps:
Go to Settings > Wireless & Network > w=Wi-Fi Settings > Advanced > Proxy
Make sure that Proxy is black, if it is not than just blank it and save it. Somehow it saves proxy and it makes wifi browsing problematic.