I have never upgraded the ROM, so it must be 1.3. Is it difficult to remove the internal floppy and replace it? I have no idea what the components look like.
If it's 1.3 that should be obvious from the boot screen with a white background and a hand holding a floppy disk with the number 1.3 written on it! A later version would have a purple background and an animation of a disk inserting itself into a floppy drive. If you can't see this, then you have to find out if it's because of the TV/monitor you're using or if the Amiga video display itself has blown out. How is your A500 connected and to what kind of display?
I think the easiest things to do are as follows.
1. Install an external switch to allow df1: to be made bootable. I don't know if these switches are still available, though. They were originally sold by mail order companies not long after Kickstart 2.0 came out.
2. Replace the Kickstart 1.3 ROM with a later ROM.
To find out what the components look like, do some searches on YouTube.