300E----frequent failure to start

I have a 1989 300E. It is experiencing electrical failure after extended drives with air conditioning and equipment. I can jump start the car and it runs fine----and slowly discharges. Then try to restart, only to find the the engine will not turn over. Advice given---check the battery and alternator for adequate charge cycle. Also, check the voltage regulator to ensure operation. My question---concerning the prior repair of belt tensioner--a full replacement of $560.00. If the voltage regulator is the problem--did I need the belt tensioner replaced. The serpentine belt was obviously loose---but I wonder now if I was taken advantage of-----Is there a test to determine what specific repair is needed? Thanks for your assistance.