Reading your problem looks like a potential switch misconfiguration and you can confirm this with following tests:
1. Disconnect the AP and connect your laptop to the switch port to which AP was connected. Do you get IP? If yes, Is it IP from correct subnet for the VLAN that port is configured?
2. If you don't get IP, then configure that switch port as an access port for just THAT vlan from where you want the WiFi users to get the IP?
3. If you still don't get an IP from correct VLAN then flash or reset that switch port and reconfigure it to see if corrects it.
In the interim while you are doing the above and if there is dedicated DHCP server then please check if server is receiving the bootp/dhcp packets from your laptop while you trying to fix the problem. This will confirm if issue is with server not get bootp/dhcp BC packet from laptop at all or laptop not getting an response after it being sent by DHCP server.
It would be interesting to see what you end up with.