if you got a meter put it across battery and get someone to crank it over if it drops really low (which it will by the sounds of it) you know it's battery. hard to check alternator without it running need to jump start it put the meter across it when running then (take jump leads off) should be charging 13.5v to 14.5v approx any lower and it's not charging if your getting that then the battery is stuffed and not holding charge.
sounds like bad previos repair, perhaps not getting good contact at at that fuse connection