Since I'm really bored and had a simular problem:
Try this at your own fun:
Make sure your using at least OS X 10.1.5, or OS X 10.2.6
Backup anything in /Library/Printers to some folder
Delete /Libray/Printers
Then delete all the printers from print center
Delete all the Preferences that have print in them from:
/Users/YOURUSERNAME/Library/Preferences
if you can not delete /Library/Printers, run disk util first, with the "Repair Disk Permissions" option.
Next go to: Apple > System Preferences > Classic > Make sure classic is set not to run at startup.
Then
Install the latest photosmart driver, 2.0.5 from hp:
Photosmart 2.0.5
do another disk repair (get some coffee)
Restart just to make sure everything is in set.
Then start Print Center, go to Add > Select "HP Imaging and Connectivity" and add your printer. Try a test from TextEdit by typing some text in the program, go to File > Page setup and select your "Photosmart 7350" from the list. Press ok.
Now go to File > Print..
Press print, and voila, you should be working fine.
--
Now you have a tiny problem, printing in classic.
Because your printer uses HP Communications, you may have a problem with adding and using the printer in OS 9 once you have used it in OS 10. The remedy for this problem is to go to:
ftp://ftp.hp.com/pub/multifunction/software/aioscript.sit
Ive found that this script will act as a toggle for HP Communications to turn it on and off at leisure.
Now open up the classic environment by running simpletext, go to the chooser and select your photosmart driver, then double click on the Photosmart 7350 that pops up on the right. Now print from simpletext.
You may have to restart the HP communications (With aioscript!) before printing to classic again once youve printed from OS X. The new non-os9 bootable macs seam to do this seamless, however, there are some issues with the Older true os 9 classic macs.
And no! I am not an employee of HP.