Shoghunuk

I guess this won't be of much use to you but if your Mac is doing a reset loop then you are going to have to reinstall from scratch. You can't even get to the time machine options? One of the things about Macs is that they can get rid of programmes very easily but they do leave bits behind. I think your only solution may be to contact the Mac Support and see what they suggest. I don't even know if there is a Mac version of 'safe mode' and I've been using Macs for years!