Can you check to see if the battery is OK inside before you go any further. It really only is useful for a clock and if leaking I would remove it. What I do is rock them very very gently backward and forward till they snap off making sure I don't damage the motherboard. And if any leakage on the board I use a cotton bud and lightly clean with vinegar then neautralise with baking soda... And dry sometimes with a very light hair dryer. The last image I have here is for the inside for you to check.
The A500Plus is a very good games machine though doesn't have the flexibility of the 1200. I have included pictures here of available side cars for the machine plus some inside cards. The 500 series did have loads of various cards made but sadly the actual ones that go on the motherbaord are quite rare. The other thing is they are very old. So maybe hunt some stuff down on Ebay and keep a watchful eye for 500s that go very cheap cus you never know what may be inside.
The 500 was very suited to the sidecar range like the GVP for hard drive. I never really bothered with CD cus little was made for the 500 on CD. Better to use the 1200 with the CD. The OS was the 2.0+ series like the 600 in many ways so the interface or Workbench is more like the 1200, though not the same.
I would keep the 500+ as a working model for gaming and avoid messing with it too much. Check the battery and try to get a sidecar like the 590 or GVP. You could always get a 570 but I think you would be disappointed.
http://www.commodore-amiga-retro.com/amiga/amiga_scuzz32.htmhttp://www.commodore-amiga-retro.com/amiga/amiga_scuzz48.htmhttp://www.commodore-amiga-retro.com/amiga/amiga_scuzz382.htmhttp://www.commodore-amiga-retro.com/amiga/amiga_scuzz523.htmAs to the A1200 they are two a penny to pick up so don;t panic too much.
Amiga 1200 / 4000 Startup Colors?
The A1200 and 4000 perform several hardware checks as they start up. If the screen remains on any of the following colors on bootup, here is what they mean:
-Black
Opening screen
Initial Hardware tests passed
Initial system software tests passed
Final initialisation test passed
-Red
ROM error, reseat or replace Kickstart ROMS (this can also be caused by worn insulation covering the back end of the pins that connect an IDE cable to a hard drive, aka short).
-Green
Chip RAM error
-Blue
Custom Chip(s) error
-Yellow
68000 detected error before software trapped it (software or hardware error)
I think the purple screen could be the ROM maybe so could try just gently reseating them. You do know about the empty slots for the 3.1 and the arrows and they are two distinct ROMS
http://www.commodore-amiga-retro.com/amiga/amiga_scuzz102.htmJust a few thoughts there to keep you going.