Well, I wouldn't be too quick to get a new cartridge. That may not solve anything. One thing that CD's do very well, everything else being equal, is image. Especially compared to vinyl if your TT/arm/cartridge are not optimally set up. Even then its a good contest.
The critical things must be done properly, VTA (a biggy) VTF, anti skate, and cartridge alignment. You can get some fairly big changes by experimenting with VTA/VTF (by ear) once you have dialed in the manufacturers recommended set up.
Who ever said vinyl was an easy medium was blowing in your ear. Its not plug and play, but well done it can be excellent. Bear in mind there is a very good reason that folks who are into vinyl will pay big bucks for turntables and arms. They are not just rich and /or foolish. You can only expect so much out of a modest rig.
Get out you alignment tools, your arm level, your platter level, and your VTF guage and have at it! :-)