B737 Captain reports shutting down the number two engine after push back to allow more bags to be loaded. The attempted restart is unsuccessful with smoke reported coming from the engine by passengers and ground crew. A nose tire is damaged when it makes contact with the tow bar after a tow bar malfunction.

Narrative

[We] pushed from Gate to Spot 5. Started number two normally; during number one engine start; late bags arrived so I shut down number two engine. Bags were loaded and; when starting number two engine the second time; could not get N2 rotation. We cycled packs and bleed switches and tried again to start number two engine. Ramper on the tug reported smoke from the number two engine and Flight Attendant told us passengers reported smoke from the right engine. I told Rampers I would like to be towed back into gate. I called Maintenance and told them about our problem and that we were coming into the gate. The First Officer got clearance from Ground to go back into the gate. I then talked to the Ramper on the tug again and released the brakes. The aircraft rolled forward and the Tug Driver told me to stop the aircraft and set brakes. He then told me the tow bar was broken and they were going to get another one. I then realized I needed to shut down the number one engine and did so. A new tow bar was brought out. We were towed in. Maintenance came out and told us they were replacing the starter on the number two engine and a nose tire.