I'd start by changing the battery. A 6 year old battery is pushing the life it, not using the car much is bad for the battery, like it was stated previously. Car batterys have an average life of about 5 normal years of use, +/- a year or two depending on use and state of the cars charging sysem.
Take the battery to a autozone, napa etc. and have them check to see what shape it's in.