When I play music through my MINI JAMBOX the sound is really weak and has a lot of static in the background. The device...

Have you tried a bluetooth reset or a software update? Here is a link to the soft reset: Jambox Reset and here is a link to the software update mytalk.jawbone.com

It sounds like your MINI JAMBOX is not holding a charge. If you've tried multiple USB cables with no results then the issue could be with the USB port itself. This port is not too difficult to replace if you follow this guide: USB/Auxiliary Port