I got a 2007 Toyota Sienna and its was starting fine until I tried installing reverse sensors. Wont start now.

Using a light tester i found both reverse fuses are blown (will replace those later). But heres where it gets strange, I jump the battery and car starts, everything works well, but as soon as I remove the cables the cars shutsoff instantly. For testing purposes I removed the old battery and put another heavy duty one in (temporarily), and I took the car for a drive. I drove around the block a few times with no problems (10 mins maybe). Now my question is should I get the battery tested or purchase a new battery or do you guys think the alternator may not be charging my batteries. I can keep driving on the temporary baterry and see if it gives up that way I know for sure if the alternator is screwed up.