New ink only prints pink and black?

Try soaking printhead in the cleaning solution and it will resolve the issue. Check out the video on how to repmve printhead below. Put it in about half inch of solution which is 50% water, 40% window clening solution like windex, and some ammonia or rubbing alcohol.

For severe HP OJ 6500/6500A print quality/missing color issues there could be an air bubble in the ink cartridges, air gap between cartridge and PRINTER, or a portion of the PRINTHEAD is dry, so you should first perform a Clean PrintHead procedure from your printer control panel.
NOTE: If one or more the colors were previously dry fired during printing (i.e. if you continued printing using only a few colors to one, air may have been accidently ingested into the ink lines between the cartridge(s) and PRINTHEAD. To recover from this problem, you may have to run the Clean Printhead procedure 2-3 times.
If a problem persists then it is suggested to review the steps outlined on the following HP 920 support pages, including printhead removal/printer cleaning and service station cleaning. It is suggested you refer to printer manufacturer instructions first as the Inkjet411 procedures are provided for general guidance purposes only. A dirty service station can cause poor image quality and/or ink cross-contamination between different colors:
http://inkjet411.retailinkjet.com/?page_id=1495
If the problem still cannot be corrected, then the PRINTHEAD may be dry and may need to be flushed (i.e. with warm water as it could have dried out, but this is a function of how much you print). Remove and soak in hot water for 5 minutes...thoroughly dry printhead prior to re-installing. Retest. For more information please visit:
http://inkjet411.retailinkjet.com/?page_id=856
Worst case scenario the PRINTHEAD may simply be electrically damaged or at end-of-life (typically fails between 3,000 and 5,000 printed pages) and may require replacement, usually accompanied by error messages like Incompatible Printhead or Ink Delivery/System Failure. NOTE: The PRINTHEAD will eventually fail in time. For more information on the how the PRINTHEAD works, watch the video here: http://inkjet411.retailinkjet.com/?page_id=1983
To verify Printhead performance, run the Tap 41 diagnostic test, (Pen Status: Pen OK).....for printer model instructions please visit:
http://www.Inkjet411.com

It's possible that your new ink cartridges are actually dried out. I know, they're new but I had 3 out of 4 shipped from a major supplier once and even though it all looked good 3 cartridges were actually a little dried out. Sometimes all it takes is a couple drops of water to get it going again.

I that doesn't work ty this:
More than likely your running out of ink. Check the ink levels first.
If you have Windows 7 you can check this by clicking on the "Start" button at the bottom of the screen, click on the "HP" folder and click on "HP Solutions Center". A graft will come up showing you the printer cartridges levels. Click on the small graft chart at the top right of the screen and the graft will enlage and show you exactly the staus of the ink levels. Click "Print" at the bottom of the screen and it'll run a print test. All 4 cartridges need to be above the "Low" level. It only takes one of them to mess up the print.

If you've got plenty of ink try cleaning the printer head by:
Click "Setup" (just below and left of the LED screen) on the printer.
Scroll the Led screen to "6. Tools". Hit "OK"
Now scroll to "2. Clean printhead". Hit "OK".

This should do it..