I live in an apartment where they provide Wi-Fi, but I can't connect to the router. I turned on a hotspot and it does connect to the hotspot, but when I try to connect to the Wi-Fi it says "Windows is unable to connect to <insert name here>"
It's a Lenovo Z510, with windows 7 x64
A 'hotspot' is an open (no password required to join) network.
If the management has provided an "SSiD" and "password" for that specific free Wi-Fi, you will have to 'create' that Network in your Wireless Connections section of the Lenovo.
(They may have 'hidden' the SSiD (the Network name) and that would require you to provide the particulars before you can connect. The Network will require the "SSiD" and "Password".)
Verify with the Apt. Mgr. What the situation is on those topics.