There seem to be a lot of folks with printing problems in Quicken. Posting which version of Quicken you have may help. Where did you get the driver for your printer?
I don't print checks, but the other printing functions in 2009 R4 work for me. You might also want to visit the Quicken community. They have a separate for printing problems in Quicken, and it is very busy!
I can only speculate, but if the normal Quicken reports print without problems, maybe there is something about the check paper size or orientation or some other setting which is not compatible with your printer. Is it possible to use different formats or templates and just print to plain paper to see if you can get it to print something? That at least might be a place to start.
If you are using earlier versions of Quicken, it might be a factor.