Router and Cordless Phone Interference

We have had a router since we got DSL (Embarq - CenturyLink) about two years ago. Ever since we got the router, I have had problems with our cordless phones in my room (my room is where the router is located). The phones that are downstairs away from the router don't seem to have any problem. But phones used in my room have a lot of static and noises on the phone. It makes it very difficult to use the phone in my room... Most of the time I cannot hear what the other party is saying. We recently got a new router, and the problem persists. (I did not expect a new router to fix the problem - we had to buy a new router because our old one is failing). Setting up the new router reminded me of this annoying problem. How can I get my phone to work properly? We have the router (it is a combo router/DSL modem) plugged right into the phone line, and the cordless phone base station is plugged into the phone line using a splitter. The cordless phones system we have consists of one main base station phone (plugged into the telephone line [through splitter of course]) and the rest of the phones are on little individual docks but not plugged into the phone line. They communicate with the base station to connect to the phone line. As I said, this problem only occurs in my room, but I thought the splitter was supposed to avoid interference between a router and 2.4GHz cordless phones? If anyone has any ideas, please let me know... Thank you!