And I'm not too hot on the C-101 rear derailleur either. If it was my bike I'd replace it with a new Deore rear derailleur.

1. When you bought the new shifter did you also get new cable housings? That C-101 rear derailleur is real sensitive to any binding or crud in the cable housing.

2. If the rear derailleur was working properly before the shifter shot craps, you shouldn't have to mane any adjustment to the limit screws or to the B screw. Your problem is somewhere else. I'm betting in crudded up cable housing and/or a cable tension adjustment.

3. Derailleur hanger alignment can also cause the problem that you describe. Shift into a gear that makes the derailleur arm point straight down and examine it from behind the bike. The derailleur arm should be exactly parallel to the rear wheel. If it's not you can probably "eyeball" a 7-speed adequately into line or have a shop align it more precisely using the proper tool.