Yes, clean the system. Also clean your games. Might take a while but games are a bitch to start if the system and/or game is dirty. The top loaders are a lot more reliable at reading carts. But if you want A/V component you have to get it modded. Since it sounds like you're looking for games, here are some that are not expensive(<$20):
Batman
Blaster Master
Commando
Dragon Warrior
Faxanadu
Freedom Force (lightgun game, so needs Zapper and be played on a CRT)
Gradius
Gun.Smole
Kung Fu
Life Force
Metal Gear
Little Nemo: The Dream Master
Ninja Gaiden 1-2
R.C. Pro-Am
Rygar
Silver Surfer
Snake's Revenge
StarTropics
Teenage Mutant Ninja Turtles
TMNT 2: The Arcade Game
The Battle of Olympus
Willow
Yoshi's Cookie