All the 80C5x chips have code space. It might not be flash, but at least you can program the code once. So these chips contain PROM with a shield over the light hole, but you can't reprogram it even if you used light, because they are meant for "one-time programming"

The 80C3x chips have non-programmable ROM. This means that the factory must embed the program into the hardware for you.

I'm going to make the assumption that in the next 30 minutes, your 80C52 chip will be garbage.

So, go and either buy an 87C52 (or 87C51) chip, or use your current one, but this time, use an external EEPROM with it, and tie EA low.