first off, get a multimeter
set it to ~20 volts. your charger should either be a 19 v 4.74a or a 18.5v 3.5a, so you need to set it to 20 volts.
put positive pin against the inner wall of your hp charger. negative on the outer wall. you should get a readout, roughly .3 volts higher than the charger is rated for. if not, if it jumps around alot (and you are sure you are holding it steady) or if its zero, your charger is dead, or the 3 prong power cord going to it is bad. those actually go bad alot, i see about 4 bad a day in my store.
next, if the power supply gave out proper voltage, plug it into the laptop. take your battery out, and now you are going to test the voltage on the pins that charge the battery. the first one, all the way left, is usually a negative. you could use that as a ground, or just one of the base or hinge screws on the bottom of the laptop. holding the black wire to a ground, use the red to test the rest of the pins. you should have a few at roughly 3 volts. if you have absolutely no juice going through, order yourself a new dc jack. they are roughly 15 bucks on ebay
solved
btw, im inebriated and used the word "roughly" alot in that...