I recently bought a Nintendo 3DS but unfortunately my University's wireless security (WPA2 Enterprise) is incompatible with the system. As such, I was looking for a way to transmit a wireless signal from my computer, and place an alternative form of security onto it (such as WEP), so that the 3DS can connect to it.
At the moment, my desktop is connected via ethernet cable, which plugs directly into a wall socket. I'm pretty unsure as to what to use, I've heard of things such as 'wireless bridges', but I'm not sure how they work. Also, I'm looking for the device to transmit a signal even if my desktop isn't turned on. Is a router my only option?
A router is your cheapest and easiest to configure option. Most modern routers can be router/AP/Bridge just by changing option.
That said are you sure they have not also locked down the ethernet port to prevent this. The key part of enterprise security on wireless is running 802.1x security with a radius server to authenticate users. They can also use 802.1x on ethernet ports.
Even if they don't restrict it I am sure they will hunt you down when they see a wireless network running WEP. This puts their entire network at risk. Most commercial wireless systems have features to automatically detect rogue wireless devices.