I'm not suggesting you use only an external disk, but rather use an external disk to test your SE. There is a small possibility the SCSI chip is bad on the logic board, but you won't know that until you do some more testing. The SCSI chip is easily blown if someone attaches a printer to the SCSI port.
Also, I don't work much past System 6 and mainly deal with Plus & earlier. I have no problem using MacWrite or Word 1.0 on a 128K Mac. And I have no problem networking with my 128K and my OS X Mac. While I do have SEs and Classics, I have had the good fortune to have good HDs already formatted. The 20MB MiniScribe was the earliest of Apple's SCSI drives and was notoriously flawed. If it is bad, it is likely unrecoverable. It was so bad in fact that when it failed, Apple replaced it with the much more expensive 40MB drive at no charge to the customer.