If I am understanding you correctly... the solder will melt if you touch it to the iron tip but will not stick, it just balls up and rolls off.

Solder balling up and not sticking to the tip... I would first blame it on a dirty tip, but if you used a brand new tip then that is probably not the issue.

Solder balls up when melted if it can not get a good bond and wet the metal it is touching. This is almost always caused by a contaminate of some kind.

Make extra sure the new tip is completely clean, if it is an old tip, it could have a little oxidation on it. Maybe try some tip tinner. It comes in a little metal container and you dip your tip in it to clean and tin it. Radio Shack carries it usually. Make sure you get lead type.

If that is not the case, the flux core in the solder could have gone bad, try using fresh flux.

Solder can get old and oxidize, but usually lasts a few years.

If you have a IR thermometer, measure the temp of the tip after its fully heated. If it is very far off what the temperature setting knob is set to, it may be fixable if the unit has a calibration screw. If it is too bad, you may not be able to adjust it enough. If the tip can reach 650* it should be good to solder with, but if the iron element is getting flaky, you may need to source a new element or iron handle.