How to get internet from wifi and share to LAN device
Solution 1:
You need to create a wireless bridge, most home routers won't have that option without a custom firmware, but i believe a few d-links I've had have actually had that option and is actually how i have my HTPC, tv and PS3 connected to my home network at home, using a cheap linksys router that has ddwrt on it it
If you need something temporary you can use a laptop to create a bridge from your wireless to your wired NIC without using any extra software, here's a guide that has some info on it from technet.
DD-WRT is a custom firmware that would be able to get the job done with any compatible wireless router.
You can find the Router database for it here, your current dlink isn't supported how ever.
Solution 2:
Check to see if your router has a wireless bridging mode (my cheap TP-Link calls this WDS bridging) in the set up. You set the network name and password to be the same as your apartment's wifi.
You would then need to to turn off the DHCP server on your router (so that your kit connected to your router get their IP address etc from yout apartment's wifi router).
You could, however, have performance problems if other clients use your router wirelessly in preference to the apartment's router as your router would be receiving and then retransmitting any network traffic.