There was a hardware diagnostic routine from Commodore and given, AFAIK, only to Amiga dealers. I haven't seen it in a long time. I think it primarily checked the mother board ports and custom chips (CIAs, Agnus, etc). Unfortunately, I can't remeber the name. I wonder if it was ever released.
Who made your accelerator and 32-bit ram? Sometimes diagnostics were supplied by the vendor. You could check the Big Book of Amiga Hardware (BBOAH) web site for downloadable disk images as supplied with your accelerator.
Failing that, there are several general purpose diagnostic and system monitoring programs on Aminet. Everyone has their favorites. SysInfo is easy to use and fairly comprehensive. Others include: AIBB, ARTM, DosTrace, Scout, SCSI_Inquire, SnoopDos, and Xoper.
Commodore included a booting diagnostic in all Amigas. The color of the screen when booting hangs up, determines what part of the process failed. I think the color code is in the manual, if not, some ppl here know it by heart.
Good Luck