Why can't I restore from a time capsule backup

The scenerio is like this:

I have a 2007 iMAC 7.1 running Snow Leopard 10.6.8 and I have been doing back-ups via Time Machine.

Recently the original 250GB hard drive started to perform slowly, so I replaced it with a new WD 2TB hard drive (process pretty smooth).

I ran the setup with the Snow Leopard DVD. partitioned the hard drive and tried to restore from Time Machine but it failed and installation just stopped in the middle.

Then I made a clean installation of Snow Leopard and do all possible updates as promoted (still Snow Leopard 10.6.8 not Mavericks) and then run time capsue. However restore was banned because "OSX version is too old on the current mac" (but actually they are both 10.6.8!!!). Has anybody come across that? Your solution please?

I then tried to upgrade the OS to Mavericks and time machine restoration this time worked initially. When I rebooted the mac the HDD space is occupied by some files (compatible with the size of the time machine backup) but there is no TRACE of any files, docs, apps... whatever... in the mac. What can I do?

Thanks!