Network troubleshooting 101. Power down the modem and the router for about a minute. Power down your laptop as well. Hard wire the laptop and then boot everything back up. If your connection seems normal at this point, try disconnecting via ethernet and starting up your wireless connection. If the connection is subpar standard operation once more, there may be interference such as microwaves or telephones operating on the same frequency. However, having just been wired in you will be directly next to the router and such interference should be a non-issue. S
So at this point, we can assume it's a software issue, as you are able to maintain a decent connection whilst in safe mode. I'm going to go ahead and assume in safe mode only the kernel and basic windows manager is loaded as well as any other specified software. And so I recommend killing processes one at a time until your connection is normal again. I'm not sure about in windows, but in a linux shell you can use pidof process name to get the process pid. From there you can simply kill pid or even the process name. If the process doesn't want to die, you can always jump to a kill -9 pid. I'm sure Windows being such a sophisticated operating system has such capabilities.