Older CD players MAY be better built - as i more solid chasis, less plastic in the structure etc - such thingsMAY make a difference in playback quality depending on the set up, amp, speakers and media. My 1st CD player only did play, pause, next track, open & close, weight a tonne with a hevay caste base etc. very stable, very accurate and was square rather than the now ubiquitous "Hi Fi rack space" wide & deep. I was convinced to get rid of it when the laser died (replacements weren't yet cheap) and now find that the tech that convinced me has it as the PRIME piece in his system.
I hang on to & havehad repaired my CD player because it is a good one and, I know this'll get a laugh, I can hear A difference that I am either used to or prefer. My marantz 52 SE is now without a motorised tray (replacement parts no longer available for the gears which crumbled) so I has a little knob put on the front of the tray so I can manually open (after pressing open for chip/prog reasons) & close it.
It plays really well, I keep it clean & it'll outlast yet another a new one.
BUT you could always buy another one if you're having trouble - then again a lot of people don't really care about the sound quality & use their DVD players as the CD player. try your discs in the DVD player & see if they play OK there.