Hey DM. The battery sounds faulty and I hope your new one works well. Check the connection as mentioned too because I had a laptop that had a faulty power switch. The company repaired it for free so check that first. It was simply a screw inside that needed tightening.

Second, the wireless network issue could be because it attached to another network other than yours. Sometimes that happens to us too and we'll connect to "Happy Family". I wonder who that is on my block? lol

Right click on your computer's wireless network's icon and click connect to network. Then find yours and click connect. If you don't see the icon, go to start>connect to> then find your network. Mine is our name so it's easy to find.

Hope that works!