Yeah that does sound like broken/disconnected antennas. Laptops have two antennas connected to the WiFi module, so it's rare for this to happen (if one antenna dies, the other one still allows connectivity, so you have to lose both antennas to experience the symptoms you're seeing). But I've seen it happen so it's not *that* rare. The most common reason is pretty simple to fix - the antenna leads have popped off the WiFi module.
Unfortunately, your model laptop is one of the annoying ones which opens from the top. To access the WiFi module, you'll have to first remove the keyboard. Service manual here; WiFi (WLAN) module access instructions are on page 61.
http://h10032.www1.hp.com/ctg/Manual/c04409502
The WiFi antennas have a round plug which simply presses into one of two round sockets on the WiFi card. They're held on by friction, so it's not unheard of for one or both to pop off. When both come off, the symptoms are exactly as you describe. Simply place the plug over the socket and press it back on. If it feels loose and you're afraid it might come off again, you can use a piece of electrical tape to hold it in place.
http://www.insidemylaptop.com/images/Dell-Inspion-N5110-disassembly/Dell-Inspiron-N5110-disassembly-22.jpg
Edit: Found a better pic which shows what the WLAN card looks like with and without antennas attached. The antennas are the black and grey cables.
http://forum.notebookreview.com/attachments/to-nettverkskort_72359a-jpg.109957/