I ended up throwing away the first batch of yeast starter as I left it for almost a month. When I opened the container though it smelled fine and saw no signs of infection. I don't know if the yeast was still viable but I wasn't going to take the chance.
I bought another smack pack of American Lager and used that and made a 2 liter starter in my new Erhlenmeyer flask, and while my stir plate is not ready, I used the magnet to stir it and loosen it manually, as well as frequent swirling. Whether I got to the recommended quantity of yeast I don't know.
I made my batch, which came out to 1.054, and put both the yeast flask and the carboy into my cold room and that went down to about 54 degrees, and I pitched. Overnight it got really cold outside and the room was down to 48 by morning, and the carboy with yeast was at 50, and it has stayed between 50 and 52 ever since. The visible activity started about 12 hours after pitching and was going strong by 24, and really took off by 36. Today, 3 days later I still have a strong fermentation going. All carboy temp readings were with a stick-on fermometer, but the one time I calibrated it was surprisingly dead on.