Here are the instructions for swapping printer cartridges:
http://h20566.www2.hp.com/portal/site/hpsc/template.PAGE/public/kb/docDisplay/?sp4ts.oid=306884&spf_p.tpst=kbDocDisplay&spf_p.prp_kbDocDisplay=wsrp-navigationalState%3DdocId%253Demr_na-c00033431-1%257CdocLocale%253D%257CcalledBy%253D&javax.portlet.begCacheTok=com.vignette.cachetoken&javax.portlet.endCacheTok=com.vignette.cachetoken#N100BB
InkJet printers are basic in design:
http://computer.howstuffworks.com/inkjet-printer.htm
InkJets need two basic components to print, a cartridge and a print head. Your 1300 uses cartridges that appear to have print heads included in the cartridge. Thus anytime you swap one you swap the other too. If multiple cartridges produce no output then your printer may have a power failure where it is not able to force elctricity to the print head to apply ink to the paper. That or you coincidentally have a lot of bad cartridges/heads.
The best test here would be to grab a 2nd 1300 and compare the cartridges. If the cartridges work in the 2nd 1300 then the printer is the problem. If the cartridges do not work in a 2nd 1300 then the cartridges are bad. I'd guess you dont have access to a 2nd 1300 to confirm but if you do that is how you would know for sure.
Anytime you are dealing with output issues make sure you are not using refurbished cartridges. You need to use new cartridges to rule out a defect in the refilling/recycling process which is fairly common.
Worst case scenario your printer looks like a small and cheap model that is designed to be expendable. Trash it and pick up a new one once you have met your troubleshooting threshhold.