To elaborate a little further:
You should be able to convert just about any image to one that will burn and run properly on your DC. You will NOT be able to do this without doing some tinkering from a command prompt (I'll assume DOS) -- there is no push-a-button-and-it's-ready solution. You're also probably going to generate a lot of coasters in the process of learning how to do this, so get used to the idea.
What your DC is detecting is a particular disc format -- one or more audio tracks followed by a data track, which is the format that most cracked DC images have. The burned/not-burned status isn't the issue -- you can burn all the CDR audio discs you like, and the DC will see them as single-session audio CDs and play them just fine.
What you need to do is convert your disc images to ones that have the data track first and then the audio, and bin2boot is one of the primary tools for doing so. (The FAQs pointed to in this thread describe the other tools of the trade, such as cdi2nero, mkisofs, and cdirip.) You're going to have to take your CDI/NRG images apart (using cdirip, CDMage or ISOBuster, or Nero if you've already burned the disc whether it works in your DC or not), tweak them as described in the FAQs, use mkisofs to create a new .ISO from the tweaked files, use bin2boot to turn that into a .CDI image, then cdi2nero to convert that to a Nero NRG that should now play on your DC.
<bill_cosby_voice>
And if you're not careful, you might learn something, too. Now eat your Jell-O pudding...
</bill_cosby_voice>