Hmm, that is a bit more beyond the scope of my knowledge.
Are you getting to an actual disc screen? How will it load with out a disc in the tray? I believe it sends you to some menu if you do not have a disc in it IIRC. It has been a while since I tried anything like that since I use the action replay and it boots you to a separate screen instantly.
If its hanging on the disc I would more so believe its the disc drive, however if it is hanging before the disc is loading then there might be more serious issues in your system. Though I never really heard of a saturn just crapping out before (not that its not plausible). Most of the stuff I have heard of is bad disc drives.
EDIT: Just did a small amount of research. The majority of problems come from the disc drive laser failing or the motor starting to fail. However it could be that the bios might be having some issues, but if you can get to manage memory (and if your battery is not dead) then it is not a bios issue. However I have seen a couple people bring up that the caps might be bad. I would look for bulging caps. The only problem is that the caps used in the saturn do not always bulge when they fail. I can not really help you beyond the scope of that as I am more of mechanical guy not electronic. Also as one more question, is the disc acting weird when loading? Sounds slow, or something? I am pretty sure there is a way to trick the saturn into believing the disc tray is open to check if your laser is working properly or not when spinning a disc.