My second son situation sounds like yours - when I am busy with Dylan, I let him play on the PC, watch tv or play on his Leapfrog Explorer. Although I will chase the kids outside or at least off the screen time if I feel they have been on it too long at one go, I don't really put serious time limits - they are learning all the time while screen time is going on, and their only real "down time" on the screen stuff is watching TV when they choose to watch a movie or the kids channel.. even the kids channel here (BBC - CBeeBies) is all educational shows in effect.
you can find some awesome games and sites out there for him to play on while you are busy, then everyone is happy, and when baby is sleeping you can do stuff with him. This works well for us.
