Freekin' HP! They used to be the best.
I gave away my last HP inkjet a while back and I haven't kept up with there product line but...
It sounds like you have a compatibility problem between your ink and paper. Are you using archival inks? If so, you have to use paper designed for them... slow drying ink is a good indicator of pigment base inks on paper designed for dye base inks.
Make sure your paper and ink are made for each other... if that's not the problem, you could have contaminated ink.
I used to love HP printers, especially their lasers... I'm an Epson/Canon convert now... I still don't used their inks and paper though.