@PierreM59 If the computer cannot operate on HTTPS sites, and is using current software, I don’t know there’s anything we can provide to help you.
“Some work and some don’t” seems contradictory. While sites will use different versions of certificates, the fact that you cannot even reach the site tells me you are behind some kind of “gate access” preventing you from even reaching the “some don’t” category.
If you take that same machine, and run it on a network other than where you are currently, does it have the exact same problems? If it does, then is this “gateway” that’s preventing access likely installed locally on the machine? If it doesn’t have the same problems, then it’s the network from where you’re currently operating.