some of the older, well actually now really old cd players couldn't read the cd-rs. could very well be due to the laser power. i would imagine because when such units were made there was no need to read data on a cd-r, it just didn't exist!!
the head unit in my car can read cd-rs without a problem, but it can't read cd-rws. i think it's just a matter of the tolerance of the laser reading the disc. (different wavelengths i would imagine) also older dvd players couldn't read cd-rs/ rws. my cheap o samsung dvd player from 99 couldn't read burned VCDs i got off ebay, but it plays stamped vcds fine. that's why some if not most of the new dvd units denote the capability to play cd-rs and cd-rws.
the stamped cds and burned cds are different in nature, and even cd-rs and cd-rws are burned at different wavelengths, which could explain cd-rs being read yet cd-rws could not.
i'd say have three options:
1. play only stamped cds on your way old cd players and stop pirating music!!

(yea there's a joke) because i doubt using a different burning player would do anything for ya.
2. buy a new cd player.
3. try different cd-r medias, the way the medias are made can reflect the laser differently (big maybe), so it just might be read by your older cd /dvd player.
that was long huh? hope that cleared it up a bit, and i'm sorry you might have to spend money, but you can try to get the apex-1200 for around 50 or the 3 disc changing 5131 for like $90 (that one plays everything.. only if i can figure out a way to get to the hack menu...