If specific buttons on a laptop keyboard do not work then there are a couple of things that can go wrong. The first thing I always check is the connection between the ribbon cable from the keyboard and where it plugs into on the motherboard. Generally a loose connection will cause a larger portion of keys to stop working, especially if one or two lines from the cable are not fully plugged in. Use this guide to find out how to get the keyboard out and check the connection. Additionally look at the connector on the motherboard and ensure that there is nothing shorting any of the pins, like a stray piece of metal or possibly some sneaky liquid. If you do see something like liquid on the motherboard then use a q-tip and Isopropyl Alcohol(The kind you get from any drug store).
If this does not work then your best bet is to purchase a new keyboard. They are not very expensive and a better option then popping off the keys and checking for obstructions, and then trying to put them back on again. I've seen people do this and they ended up either breaking the hinge for the keys or removing the plastic plunger underneath the key and then trying to glue it back on, guaranteeing that the key will not work again.
If you want somewhere to start to find which keyboard to find, HP was nice enough to use HP specific part numbers that all end in -001 so that you just have to Google it and purchase the most reasonable part. To save you a little more time, I believe that the model for the keyboard is 535689-001.