As a mechanic of 20 yrs,my opinion is the battery is useless,however try this,jump start the car then while engine still running,disconnect the jump leads and if it stays running then the alternator is OK, if after say 20 minutes of charging the battery you switch the engine off and it wont restart then that will prety much confirm a dud battery.The theory behind this is you need power to keep the electronics running so if it runs with the battery dicsconnected (after you have jump started it) that means the alternator is working as it is supplying the power to keep the engine running.Lastly if a battery is discharged and possibly a very old one at that,sometmes when an old battery has gone flat it will never recharge,Hope this helps,any more info contact me thru tonylawleruk@aol.com
Tony
March 2008