2007 Ford Focus car won't start

This first started about two months ago, jumped the car, took it to ford dealer, they said it just needed a new battery, we installed on. Now it died again on my way home from work last night, lights dimmed a few times then engine died. Today I had a friend try to jump it, it starts initially but dies after about 5 min. When I try to start it w/o jump it tries to turn over and the windshield wipers come on (note we turned off all electrics we could when jumping, so no reason for wipers to come on). When the car died originally we thought it might be the alternator, and now that the new battery died so quickly I was thinking the same, but I have never seen an alternator problem cause wipers to come on. Any suggestions would be greatly appreciated! Thanks!