Color Cartridge light is blinking.Cartridge is about one week old.Black one is working fine.

that is because ur head of ur printing cartridge is damaged.

remove ur cartridges black as well as color
n install only black cartridge n check d blinking of lights on ur printer if it doesn't blinks it's mean ur black cartridge is OK but ur blinking of light on ur printer is same it's mean ur head of black cartridge is damaged
after this process remove the black one cartridge and install the color one cartridge n check d blinking of lights on ur printer if it doesn't blinks it's mean ur color cartridge is OK but ur blinking of light on ur printer is same it's mean ur head of color cartridge is damaged
now take a dry cotton cloth n gently clean ur cartridges head install both cartridges on ur printer n check ur blinking light on ur printer that will work only if u r too lucky other wise u have to purchase a one cartridge.

Thank you for suggesting that the cartridge might be bad. I almost got rid of my deskjet D1320 because it was blinking continuously and I could not figure out why. I tried everything from new driver to looking for a paper jam and nothing worked until I tried your suggestion. I tried each of the cartridge separately to find out that the black cartridge was making the light blink but not the color on. I replaced the black cartridge and the printer is fine now

no, there is no way for it use any old 22no. color cartridge.

One or both print head are defective.Open cover put out color cartridge then close cover.If blinking stops replace color cartridge.If blinking continues put out black cartridge and put in color.If blinking stops replace black cartridge, if not stop replace both cartridges.

Sounds like the JEt for the Black might have clogged or the print head has malfunctioned.

i went to the hp website and they acknowledge this problem they have a page on this http://h10025.www1.hp.com/ewfrf/wc/document?docname=buu02180&cc=us&lc=en&dlc=en&product=59273

it appears that there may be dirty contacts in the printer as well, i changed the black cartridge and it started working, just luck i guess

The light you describe is the ink light.
When that light is blinking, try this.

Turn on the printer. Open the front cover and look at the carrier for the ink cartridges. There is a white arrow right above the latch for the color cartridge.
Once the carrier stops moving, the white arrow should be pointing to a symbol which represents the problem (the reason the light is blinking.) Examples are low ink black, low ink color, sick black ( replace ) , sick color ( replace ).

IF you have just replaced your black cartridge, you might need to replace your color cartridge too.
This printer will not work without both ink cartridges installed and full.
You cant print with a full black and an empty color cartridge unfortunately, even if you only want to print black.

Hope this helps!

clean the carriage home
check the data cable for the carriage home
check the media sensor on the left of the plotter media bar

The black printing usualy occurs when there is a faillure in the light, since your light is working fine, there may be a problem in the imaging device inside(camera) or the reflector. There is nothing wrong with the cartridge.