CRJ50 Captain reports departure delays due to weather and late arriving crew members. Once airborne the flight is unable to reach their destination due to the line of thunderstorms and diverts. Duty time limitations result in the flight continuing the next day.

Narrative

At the gate; we were delayed an hour; until all 3 crew members came in. The plane was there but with a deferred APU and a line of thunderstorms were coming. We boarded and fueled the plane. We asked for an extra 500 LBS of fuel; as we thought we'd be delayed at the gate. If we came back to the gate; I would have timed out; as my duty day was stretched long. We pushed back and the airport closed until the storms passed. At that point we called Dispatch and moved out contingency fuel. We had enough for minimum fuel for takeoff. We also got a new clearance. Dispatch and the crew were ok with the route and the fuel. After takeoff we headed north approximately 80 miles then east. The storms built to our south in an east/west line. We couldn't break through. Fuel became an issue and we spoke to Dispatch over the #2 radio. All of us agreed we wouldn't make it to destination and chose an unplanned alternate. We diverted. Timed out and completed the flight the next day. I later called in sick; as it was day 6 and was fatigued; but I wanted the money. Fix the APU; staff airline properly; study weather patterns for the area; as well as interpret the TAF's.