Edit:
Wait, you asked if something could be allowing the internet to work only in your home... That could be a proxy specific to your internet. Go first to Internet Explorer > the cog icon at the top right > Connections tab > Setting and LAN setting. Make sure those two don't have all options inside unchecked. Take records of the numbers in the boxes first. Now try IE first. If it works, try FF. If it does not work, go to Options > Network tab > Settings, and make sure "Use System Proxy Settings" checked.
Good luck.
I am also thinking it may be proxy related. This is what you should see when you follow Smart_Guys instructions. Have you tried connecting a different device to the hospital network? Also check for the latest drivers for your WiFi card in your laptop which is an Intel Centrino Wireless-N 1000 Acer Aspire 5740-5513 Specs - CNET and you can the drivers on Intel's website using their driver update utility Intel® Driver Update Utility