How to access an older Time Machine database.

We had problems with my wife's iMac and so I reinstalled the operating system However, since I wasn't sure what the source of the problem was, I chose not to do a restore when the new system installed and so it created a new Time Machine database starting at that point. I've checked the disc using finder and the previous data is there, but Time Machine refuses to access it. How can I get Time Machine to look at that data?