replacing a Trek 4300 bottom bracket with a new one
The new bottom bracket will fit as long as it is of the same thread and type. The Trek uses an English thread bearing. Shimano also says that you must use a mountain bottom bracket with a mountain crank. The new crank must be pretty close to the same tooth count as the original. The front derailleur is designed to work with a limited range of ring gears. If you are in the 40-44 tooth range you will be fine with the original derailleur. It may require some adjusting as the chain line most likely will be slightly different. I recently did a similar swap and I had to move around  the bearing spacers to adjust the chain line.