Upgrade HDD using Time Machine, but no Snow Leopard DVD, only Leopard installation DVD = kernel error on startup

Hi guys and girls.

Background

I have a MacBook Pro (March 2009 vintage). It was loaded with OS X Leopard on a 250GB HDD. When Snow Leopard was released, I upgraded using a DVD bought from Apple. In time, I added an external USB HDD to use for Time Machine Backups. I am now, however, knocking up against the capacity limit of the original hard drive.

Given the above, plus the fact that I no longer appear to have the Snow Leopard DVD (upgrade version I believe) - what is the recommended way to get back to my old setup (files, OS, settings etc), but with my new, larger HDD?

So far I have tried:

1. Formatting new HDD as Mac OS Extended (journaled), GUID partition having booted using my original (Leopard) installation DVD. I then selected the latest Time Machine (Snow Leopard) backup. After a couple of hours of restoring from that backup, the system restarted, but had kernel errors on bootup.

2. As above, but when formatting, chose to zero all data. This had the same end result.

Questions:

1. Are the kernel errors I'm experiencing due to the mismatch of booting off Leopard and restoring a Snow Leopard backup?

2. Would finding my (or even a) Snow Leopard upgrade DVD help? If so, how?

3. What am I doing wrong generally? I do like to try to understand these things!

4. As above, what is the recommended way of doing what I'm trying to do, given the limitations of release DVDs etc.

Many thanks