Dustin Houk, The battery, cable/charger or charge port may be faulty damaged. Look in the charge port and blow/pick out(carefully) any dust/debri that may be causing an issue also look in the port for any bent pins and straighten very carefully with a tooth pick. Try a different compatible charger/cord to see if that is the issue. If different compatible charger/cord does not fix and port looks/test good, the battery or connection could be bad, if able to clean battery connections and reconnect/install battery, still not charging battery probably faulty(link #3 replacement battery). If port is found to be bad/loose/damaged , this is really not a repair for the inexperienced because the charge port for your device is soldered to the mother board and the heat generated could cause further damage if not very careful. I will post a link to a tear down guide to get you inside the tablet to check the charge port. The whole mother board can be had for less then $20.00(link#2) and may be the way to go if port was bad. If not wanting to do the repair yourself have a good computer/cell phone repair shop have a look and estimate repair. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
http://www.waoweo.com/samsung-galaxy-551/disassembly/videos
http://www.ebay.com/itm/Genuine-Samsung-Galaxy-551-I5510-Motherboard-GH82-05279A-/332105057011
http://www.ebay.ca/itm/Battery-For-SAMSUNG-Galaxy-551-GT-i5510-GT-I5510M-GT-S5250-GT-S5280-/251947564245