How to resolder a broken connection for an LCD component
If you're completely new to soldering, this isn't the best situation for your first attempt. But if you're feeling brave, here's what I'd do:

Clean off the old solder, and broken-off fragment of the lead, from the large pad on the PCB. To do this, apply some flux, heat the pad, and when the solder is liquefied, use a tweezers to pull off the old foil strap. If you have solder wick, that can help remove the old solder, but if not, some stranded wire can do the job. You don't have to get all the solder off, but try not to leave a large blob there.

Get some stranded wire (24 gauge or so), strip 1/2 inch insulation off the end, and solder the end onto the large pad. Use fresh solder, and flux. You're doing this end of the repair first because it requires more heat and won't come unsoldered as easily when you do the smaller end.

Now cut the stranded wire, leaving enough to bend downward to reach and contact the small strap coming from the smaller board. The wire needs to be in contact with the strap during the soldering operation. A small hemostat or alligator clip could help, but you probably don't have those, in which case you could even wrap a single loose strand of wire around to hold them together. Then use flux and solder to make the connection.


Good luck!