Excellent, that's very helpful. At what temperature are you fermenting the beers?
Regardless, you significantly underpitched the one with the liquid yeast. The rule of thumb for pitching rates is 4 billion cells per 5 gallon batch per point of original gravity, for ales. For lagers, double it. In your case, for a 2.5 gallon batch of 1.034 wort and lager yeast, the optimal yeast cell count would have been:
4 billion * 34 * 0.5 * 2 = 136 billion cells
1 smack pack, fresh from the factory and 100% viable, provides 100 billion cells. Since yours was 3 months past its expiration, your viability was likely abysmally low, likely in the 30% range, meaning you pitched 30 billion cells, or barely 1/5th of what you should have pitched. The yeast are stressed and are struggling to multiply to the necessary cell mass. I'm sure it will still ferment, but it's going to take a while, and you'll likely notice some distinctly "un-lager-like" flavours in the resulting beer. Next time, make a starter, using a site like
Mr. Malty to calculate the appropriate size starter.
Lagers also need lots of oxygen. Shaking/splashing/stirring/aerating with a pump are more than adequate for ales, but to truly have a good lager fermentation, you'll need to consider an oxygenation stone. You can still make lagers with what you've got, they just won't be as "clean" if you'd hit it with pure oxygen.
Lagers are a special kind of beast, they're much more sensitive and temperamental than ales, but they can be very rewarding when you get it right.
Also, get in the habit of rehydrating your dry yeast.
Here's the manufacturer's data sheet for the yeast you used, which explains their recommended rehydration procedure. Sprinkling dry yeast directly into the wort can reduce cell viability by up to 50%, and as I just outlined, lagers can't afford any reduction in yeast cell count.