have an Imac late 2013, was running El Capitan, upgraded to Catalina without doing anything about El Capitan. When I try to login, it accepts password and then goes into a endless loop. Tried first aid in utilites and tried to downld an older os .

It definately needed a wired keyboard, after getting to the disk utility I could not find how to bring up anything relating to HFS Extended GUID but did have three separate computer symbols showing Macintosh HD, another showing Macintosh HD-Data and one with MacOS Base System. I clicked on the Data and that showed it was a GUID partition so took a chance and deleted that one and then it allowed me to download Catalina again but did not allow me a choice of OS's. So did that and then it allowed me to go thru setting it up. And asked me to download either from a time machine or another computer so did that from a laptop and wonder or wonders it all works! Thank you all for your skills and taking the time to help those of us who are tech challenged.

FYI it was getting on Wi-Fi even tho when I put the password in to open up it would go to an endless loop with small rotating fan and even the spinning beach ball, works fine so far today. Thanks so much for your help.

My Imac from 2013 had several problems including it refused and said it was not capable of moving on from El Capitan so I went into Backmarket and bought a 2019 Imac refurbished and am quite pleased with that. Thought I would try and get some use out of the other and that's when I ran into trouble. I do have a laptop from 2012 and the other Imac but the ones I described are what shows up on Disk Utility when you go to First Aid etc. Had already downlded and moved all important stuff to the newer Imac so had no problem with losing data if I erased wrong partition but it worked! Have no idea why it decided to let me downld Catalina but it worked and solved a lot of problems that were in El Capitan,