Any tire plug/patch kit will come with replacement valve cores and the tool to pull them out and put them in. Sometimes Slime can gum them up and the valve wont seat properly. If you have slime in the tire make sure the valve stem is in the 12 o'clock position to reduce the chances of he new valve core getting clogged as well.
Check with your local bike shop, first. They will probably swap the core and pump up the tire gratis if you look like you'll buy a helmet or something from them in the future.