I have a really old 1x burner myself, and back in those days, I HAD to burn a PSOne game at 1x or it wouldn't work well (though it'd usually start up, FMV movies would usually skip at parts, and it had a high percentage of crashing during some loading sequence). So I thought it'd be the same old story for my PCE, so at first I always burned them at 1x as well.
However, after reading around a bit, as Seldane said, modern burners supposedly give just as quality burns at their respective lower speed cap, like 4x, like the old ones did 1x. So I've been burning 4x with my "newer" burner for my PCE games, and they all work fine. (I've yet to try a 4x burned game on my old Playstation 1, though).
You may be doing something wrong during the backup/burn process. If you're trying burn a downloaded copy and that's not working, try backing up a 1-to-1 copy of an original disc you have and see if that works. A 1-to-1 backup copy should give you the highest percentage of it succeeding -- if that works, you can blame the bad download. If it doesn't, try changing the media or try burning it elsewhere and see if it gives you the same problem.
I noticed that my PCE Duo is really sensitive to the type of media I use, but all of them DO work. Some just make very light scuffing-type noises as they spin.