I don't know if this helps, but I was having the same problem, it only started after I did an update and was asked to put buy.garmin.com, my.garmin.com and connect.garmin.com into my trusted sites, from that point garmin connect stopped working. Checking further I notice that garmin connect is not a https site and therefore shouldn't be included in the trusted sites as it only accepts 's' sites. When I deleted it my access to garmin connect was restored. I don't know if this the correct way of doing things but it worked for me.
I don't know if this helps, but I was having the same problem, it only started after I did an update and was asked to put buy.garmin.com, my.garmin.com and connect.garmin.com into my trusted sites, from that point garmin connect stopped working. Checking further I notice that garmin connect is not a https site and therefore shouldn't be included in the trusted sites as it only accepts 's' sites. When I deleted it my access to garmin connect was restored. I don't know if this the correct way of doing things but it worked for me.