For seedlings, you don't need too much really. You don't need fans blowing on them, they don't smell, and they don't need a whole lot of light.
With a 2'x2'x1' space, you're not going to fit much in there for ventilation (or even lighting)
What I would personally do is use that space for seedlings, have a light source on the outside that focuses in, and maybe a fan blowing lightly into the space from the outside just to keep airflow moving and to help stabilize temperature and humidity. You could probably use a standard CFL or 2 here since it would only be for sprouting and getting them to grow a little bit before moving them to a larger area. Since the space is white, I don't think you'll need to put anything down like mylar or any reflective surface covering.
Once the plants get to the veg stage, they need actual light, and I don't think you'll be able to adequately provide lighting in there while keeping temperature and humidity where you want it (I think it will heat up quite a bit, and that small of an area getting damp/humid could cause mold issues within the cabinet itself since it's wood and/or particle board).
You could do some tests with a thermometer and hygrometer, plus some CFL lights to see what the temp and humidity swings in there would be, but largely, I'd probably just use it to sprout the plants, and when they get a few inches, move them to a better suited area.
Just my $0.02 on it. Good luck! Let us know how it goes
