Your information is hard to understand. For example in your OP you said "I have a backup of my mac on CCC and I just got it back from getting the hard drive replaced and when I try to boot from the backup I get a kernal panic but when I open it in Mac OS X all the files are there", which is quite different from this post where you say there are files missing on the CCC HD backup disk.
I also do not understand how you are viewing the backup disk. what system are you booting from, the internal disk? And what OS are you using, the latest MBP 2010 should have 10.6.4?
When installing Snow Leopard on a disk that already has a system and users folders, the installer does not overwrite user data, it does a type of archive and install, with no old system folder like Leopard had, so your data should be OK. However, if as you say, there are empty folders then the data in those folders may already be gone or they may still be there with the invisible bit set so yu can't see them.
Without ccorrect information it is impossible to help you without further risking data loss, However, if you are now running from the internal disk with OS 10.6.4, you should be able to just drag any existing data from the external disk to the internal HD.
Sorry i can't be of more help.