732 cycles-wow! As long as your showing a Full Charge Capacity of nearly 4800 mah then the cells are in good shape. The cycle count is held in the Smart Battery firmware. It is set to zero when the firmware is set up at the factory and is incremented by one every time the controller determines that a battery cycle has occurred (you can find this info by looking up TI Gas Gauge) It will never be reset unless the battery is set up on the equipment used to set/reset parameters in the firmware. No big deal, it is just a counter. Remember the number that is was when you started using the battery, then subtract the current number from that number. It sounds like one of two things here. Someone could have taken an old battery and put in new cells in it, this would leave the old cycle count intact. Or, if this is an aftermarket battery that someone programmed in their basement and didn't set up the parameters correctly. Want to know more about your MacBooks smart battery? Just google 'charlie miller smart...
Your Macbook and your charger both 'talk' to your battery. Your battery has a RISC micro and firmware that pretty much controls all aspects of your battery, it is what tells that little green light in your magsafe connector to turn green when the battery is charged. And your battery firmware can produce some really bizarre battery/charger symptoms. Before I change out any hardware I would try to find a genuine Apple branded battery that is currently working in a Macbook and give it a try. It could just be your battery. For more info see my lengthy post under 'Battery not charging or seen by OS'
Your MacBook battery is a Smart Battery. It contains a RISC micro and associated firmware. (For info on Smart Battery google 'charlie miller smart battery' and download the white paper. Your Mac and your charger (through the middle pin on the magsafe connector) both 'talk' to your batteries controller. If your battery firmware thinks something is wrong with the cells it will not allow charging. Don't try to bypass this protection, it is there to protect against fire and such. See my lengthy answer in 'Battery not charging or seen by OS'.
Yep, I've done it. (Be sure to read this whole thing, I didn't put all the info in a good order.) Bought one of those cheap after-market batteries and it wasn't long before the firmware screwed up and my MacBook started displaying all sorts of bizarre symptoms, related to the battery. So here I had an almost new battery that the firmware was messed up in and an old Apple branded battery with worn out cells. I did what any redblooded engineer would do and took both batteries apart. This is not easy to do. Apple glues the cells into the bottom of the battery holder and they are tough to get out. I used a paint scraper to get them out. Still damaged one of the cells, but no matter cause they were trash anyway. Take your time and you'll get them out, just be carefull not to damage the board in your original Apple battery. Ok, you got all the cells out of their cases. Apple uses spot-welding to attach the tabs of the cells to the board (the correct way). You can't remove the tabs without messing up the board so...
This all sounds quite familiar. I've spent the last couple of months investigating battery 'problems' on my own machine (White macbook, early 2009). My original battery had well over 400 cycles on it and, of course, couldn't hold much of a charge. Checked into a replacement; Apple battery-$129, Chinese battery-$32. I opted for the Chinese battery, after all, a battery is a battery, right? My new Chinese battery worked great, 4+ hours of use on a full charge. Then at about 40 cycles or so it started acting really strange. Like it would charge up, then while using the machine on battery it would shut off and not start back up if you just put it to sleep. There where many different symptons. I of course I read all the forums and tried all the 'fixes'. No luck. Finally one day I got the dreaded 'X' through the battery icon and it would no longer charge. The interesting thing was that the machine was running on battery! Click on the battery icon - 'Power source: Battery---No Batteries installed'!! Your MacBook...