I changed the spark plugs and the cylinder 3 ignition coil on the car a month ago. Right after I replaced the coil, the car wouldn't start but would when jumped. Over the course of the month, it has started fine with a few exceptions. What happens when turning the key is that the engine will try and turn over but doesn't seem to have enough power. I was always able to jump it until most recently when I hooked up the cables and it seemed to make no difference whatsoever, even after letting it charge for a long time. Is there a common connection between an ignition coil replacement and this issue? Hopefully I have provided enough information--- any help would be immensely appreciated.

It wouldn't surprise me if you only needed a new battery. Most auto parts stores will test old batteries for free. If you need a new battery, have it charged prior to installation. Be sure to clean the battery terminals and connections with abrasive cloth. There's no connecton between the coil and your current problem.