How to fix my computer so that I can connect to the Internet?

I'm a college student using my dorms Wi-Fi. Recently, whenever I try to use the Internet on my Lenovo laptop (windows 8.1) the message "DNS Lookup failed. No such host is known" appears. My roommate has not had these problems and I can connect to the Internet on my iPhone. I've had this issue on both Internet Explorer and Google Chrome. I have tried disabling the proxy and resetting the DNS but neither has worked.

Well, you can't carry a laptop around and merely click on the browser to connect to the internet.
There's a list of connections available to use where ever you may be that are within range. But the laptop must initially be set up for wireless use in the Network and Sharing Center under the heading of "create a new wireless connection.". If you have done this then you will only have to click on the wireless icon to see the list of available connections. Click on the schools wireless connection and enter the password, if needed. Any browser will work once you have an accessible connection.
Also, your school deals with this frequently and they will assist you in getting on line and into their server. They will issue you a school email address most likely.

Try a usb wireless adaptor. They are cheap and work well.

If you really want to fix this you'll need to gather some data first.

1. Check your Wi-Fi adapter's properties and make sure you don't have hard-coded (static) DNS info. Control Panel -> Network & Sharing -> Change adapter settings -> rt-click on your Wi-Fi adapter and select 'Properties' -> then dbl-click on TCP/IPv4 -> Make sure both sections use the "Obtain…" setting. Click Ok to get out.

2. If you changed something in Step-1, reboot and come back to this step. If things looked good in Step-1, open up a CMD window (Start button, type CMD, hit Enter) and type: ipconfig /all -- and ask your roommate to do that command, as well.

3. Compare the Wi-Fi adapter sections and make sure you're getting an IP address in the same range as your roommate, a similar subnet mask and default gateway; but especially check out the DNS server info. Update the bottom of your question on the results of that comparison and whether you had to make the changes listed in Step-1.