muffler install should not effect starting as described. make sure when you turn on ignition you wait a moment and listen for fuel pump to build presure and shut off. you will hear it stop and then crank it over, shud "pop" right off

 

I put the Rush 1.75s slipons on and a PC-V on my 2008 Fatbob. I noticed right away that it had to crank a couple of rpms more than stock if you let the light come on. If you turn on the key and crank it right up it is better to start. Mike

 

Still should not crank to the point of draining the battery Like others have said could you have hit something, are mufflers tight, are there any codes showing?