Remi, in your original post you say, "I guess the cartridge isn't in too good a shape, but I couldn't tell...." I take this to mean that you do not know how many hours of use are on the cartridge, or how it was maintained. A diamond is very hard and vinyl is very soft. As a stylus wears the polish on the diamond becomes ragged and the cut wears where the diamond contacts the groove. This distortion in the original shape of the diamond stylus can actually recut the groove, destroying the audible quality of your records, forever. You should either find a Hi-Fi shop that has the proper microscope and knowledge to determine that your stylus is in good shape or buy a new one. This is especially true since new cartridges start at about $40.00. Good luck.
Marty