Ok, Since you can print diagnostic page, means you communicate from PC. Thats good!
You cannot print anything in print Queue (Browser or Applications). That means
your printer may not be designated as "Default" printer.
Navigate as follows:
Control Panel -> Devices & Printers -> You Should see Kodak C310 Icon -> Right Click Icon -> Select Make Default
Icon now has green check indicating it is indeed default printer.
Your print Queue might also be hung up. Navigate to this link and
clear your printer Queue per instructions.
https://www.printerforums.net/threads/printer-queue-view-reset.65533/
If that fails, re-install printer using Kodak install CD. Carefully follow Kodak instructions, both printed and On-Screen. Some printers require USB cable to be disconnected during install process. Read instructions carefully.
First you must remove any previous attempt to install.
Control Panel -> Devices & Printers ->
Right Click 310C Icon -> Select "Remove device"
Do that for any other 310C icon
Now you are ready for new clean install.