Barb, thanks for the thoughtful and detailed sequence of steps to follow.
Undoing the changes I made took three attempts, as I have to work fast each time. That Local Area Connection* only shows up during attempts to connect and when the negotiation fails and times out, it disappears. Nevertheless, after three attempts with reboots, it was finally undone and back to its original setting.
Unfortunately your suggested process did not resolve the problem. Of course, as expected, it put things back to 'square 1' and the result was just as it was in the beginning with the connection failing and the related Local Area Connection* IP address being an Autoconfiguration IPv4 address in the 169.254.xxx.xxx range. I tried again and checked the properties while the connection negotiation is underway, and found the 'configuration' is identical to that of the HP computer - except for the IP address, that is. The HP indicates an IPv4 address(not Autoconfiguration IPv4 address) of 192.168.137.1.
The only two times the Surface has connected with the TV were immediately following my changing the Alternate Configuration for the related Local Area Connection* to 192.168.137.1, which I chose merely because that is the address that my HP computer uses when it connects successfully every time. I knew that only one computer at a time would be able to connect to the TV, so I presumed there would be no IP conflict - and that is the same address as a few friends' computers have when they successfully connect to their TVs.
Although I had a 42+ year career in a high tech field, I am not a computerexpert and definitely not all that knowledgeable in networking; so, I do not understand why that same IP address is the one that occurs on all four 'working' connections that I am aware of.
Following the failure of the Surface to connect after completion of your suggested process, I then turned on the HP laptop again and tried to connect with it. As usual, it connected very quickly.
I remain baffled and at a loss as to what to try next. Your assistance would be very much appreciated.
Thank you.