Since it is in such sad shape, you may want to consider replacing the bottom bracket as well... They last a long time, but if the bike is so trashed that you can't remove the pedals, it could be worth the cost to get peace of mind.
Note, that changing the crank requires a puller, and the BB requires a special tool. Be sure to add those to your projected costs.
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Slow Ride Cyclists of NEPA
People do not seem to realize that their opinion of the world is also a confession of character.
- Ralph Waldo Emerson