Can't Play Games On Laptop?

I restored the computer to factory defaults to have a fresh start. I downloaded some games and this is when I realized my problem. The first instance of the problem was when I was playing a game called "League of Legends". About ten minutes through the game, the game would freeze. It isn't a computer freeze because I could still move the mouse and see people walking in place. I was then disconnected. The second instance was when I was playing a game called "Dragon Nest". I would run through a dungeon and after a short-while everything would start to move in placeI could still move freely but whenever I tried to hit something the hits wouldn't register. After about 30 seconds everything went back to normal and a lot of monsters died and I was hurt. I tested my computers download and upload speed to see if anything was different from my family desktop. My download speed on the laptop is 5 mbps, and the one on the desktop is 26 mbps. The desktop is directly hooked up to the modem, and the laptop is wireless (I don't know if this would be the reason for the difference in speed, and or disconnection/lag issues.) I have also noticed that videos on YouTube load A LOT slower than on my desktop. I finally gave up and tried to use my desktop but I seem to have disconnected from Dragon Nest on there as well (except this time it automatically disconnected me, it didn't have a pause in the game.