There's a few ways you can get this resolved. Not all easy though.
Option 1:
I'm quite surprised there's no external reset button on the AP. Did you look at the rear panel? Is there anything that could be a reset button?
If you find one, I noticed that another Engenius Ap has a procedure that you could try:
1. Unplug the power from the AP.
2. Plug the power back into the AP and count 30 seconds. At 30 seconds hold down the reset button located next to the Ethernet port for 10 seconds and release.
3. The AP will take 45 seconds to reboot after the reset button is released. Once the device has finished rebooting, you should be able to access the GUI by typing the default IP address 192.168.1.1 in your web browser.
I don't know if that will work but it's worth a try if you can find a reset button somewhere.
Option 2:
Did you by some chance turn on the AP's internal DHCP server? If so, connecting to it wireless would allow access.
Option 3:
Another option is to use a sniffer like Wireshark to see if the AP advertises itself on the LAN. If you're PC has a wired connection to a router, run Wireshark, then connect the AP to the router. Wireshark should trap the DHCP exchange. That will show you what address the AP was given. from there you could access the AP.
Good Luck!