What is important when replacing laptop batteries is the "freshness" of the cells within the plastic casing. The nc8430 is a 2006 model, so there are no reliable "new" reliable OEM batteries. I would suggest to buy one on eBay, but buy from a seller than ha s sold at least a couple of hundreds of these to ensure that the replacement cells are fresh and not been sitting on some shelf for a decade.
In order for you to get access to you data, try using a USB keyboard and mouse. If the usb peripherals work, you may want to backup your data. Secondly, in order to assess whether the problems are hardware or software related, you may want to try to restore the OS with the restore partition or use a "live" OS like Pupply Linux. If the USB ports don't work as well, then it mostly is a hardware problem and would require you to disassemble the unit (depending on your skill level).