I have a 2001 Mustang GT Conv. I went out this morning and the car wouldn't start I would turn the key and as soon as I let go, it died. Checked the battery connections, they were fine, a little corrosion so I cleaned them and reattched the connectors. This did nothing, I noticed that the radio and lights would come on though. So while it wouldn't start, it would get power, but the battery light is on. Swapped batteries from another vehicle and nothing changed. Put mine back in and kept trying to start it, it eventually started but had a bouncy idle going to 500rpm at the highest and when I would rev it to 1000 rpm the release it, it would drop to 0 and die. I noticed when I turn off the AC it will idle steady at 500, though still not as smooth as it has been. I was told it may be the alternator. Any and all help with this is great appreciated. Thank you.