Have the battery tested at a local auto parts store..most have a little hand held tester that gives a basic health reading of the battery.
Likely nothing wrong with your bike or charger. As other have suggested the battery likely has a dead short in it.
Start with the basics 1st, then start digging into the electrical if that doesn't pan out.
Current toys..
1986 Honda 350X..trail bomb!
1985 Honda 250SX..my main mudder
1985 Honda 250ES..Back in Black Trike
Current non-trike toys:
1990 Honda TRX300FW
1995 Seadoo GTX
1998 Polaris Indy Lite 340(Nearly new looking)
1998 Polaris Touring 500
1998 Club Car (electric)