Macbook pro crashed, only displays file with a question mark
Your MacBook Pro cannot find a system to boot from, hence the question mark. 

In addition, your troubleshooting was partly in error because you shouldn't have formatted the drive in exFAT format if you intend to install OS X on it.

Since you have access to another MacBook and since it appears your USB thumb drive with OS X 10.11.5 on it isn't a bootable disk, I suggest you startup your MacBook Pro in Target Disk Mode and install OS X using the other MacBook. This approach assumes the following:


the other MacBook has a Firewire port
you have access to a suitable Firewire cable


If not I'm hoping you can get access to either or both of these from your University's tech support.

Assuming you can proceed, follow these steps:


Reconnect the hard drive inside the MacBook Pro. 
Connect the two MacBooks via Firewire cable.
Startup your MacBook Pro while pressing the T key down until you see an icon floating around the screen.
Startup the other MacBook normally.
The MacBook Pro's hard drive will appear just like an external disk to the other Macbook.
Run Disk Utility to erase the MacBook Pro's hard drive so that it's formatted in Mac OS Extended format.
Now run the the OS X Installer from the other MacBook to install OS X on the MacBook Pro


NOTE: 

If you haven't actually got an installer, you can use the Mac App Store to redownload it. In doing so you'll have to log into your Apple ID account (under the Store menu) on the Mac App Store and go to the Purchased window to find the installer you want to download again. This assumes you have previously used your account to downloaded the installer at some point.

Hope this helps. Let us know how you go.