My computer connection is unreliable, do I need a new router?

My husband just changed our computer connection to At & T DSL. It was working alright for a while. My husband's computer is hook up to the cable and I got my connection through the Linksys wireless G 2.5GHZ router. I know my router is a bit out of date and there are some faster speed router out there. When we first switch to DSL, my internet connection was okay (not too slow).Like a month ago, my internet connect started to drop. Sometimes I will get like 3 hours of good internet connection and then no connection for most of the day. I have another computer next to this computer. Sometimes, that computer's router (the same speed as the one that I am using now)will work and mine won't. When I looked at the wireless network connection, it always says,"statue:connected, Duration: 00:02:46, Speed: 54.0mbps, signal strength: always 4 bars out of 5.
What does that mean? How come signal strength always shows "very good" but I don't get internet connection? Do you think someone in my neighbor is using my connection?
Sorry that I am not a computer geek. I don't know a lot of terms. Any suggestions will help but please I need simple explanation please.