Actually, I think a 95 Olds would have distributorless ignition, but use a coil pack with a fairly conventional arrangement of plug wires. My dear departed mom’s '92 Buick was like this, as is my '94 Chrysler. My gf’s falling apart '98 Honda does have COP, but I think this was pretty much the first year manufacturers were doing this.
If the starter cranks normally, but the engine won’t ‘catch’, then it either isn’t getting spark or fuel. If you determine there is no spark, I’d bet on an electronic module failing when it heats up, or possibly a relay if the ignition system is fed through one. If you have Coil-over-plug ignition, or even a coil pack, it’s unlikely that enough of the coils would have failed for it to not start.
If no fuel is getting to the engine, it could be the fuel pump is going bad. The symptoms described are pretty common for a failing in-tank fuel pump. You can listen at the tank while someone turns on the ignition. You should hear a “whizzing” or high pitched whine for a couple of seconds when the ignition is turned on.
Another possibility is if the vehicle is new enough to have a transponder key and anti-theft system, it could be disabling the engine due to a malfunction.