Time Machine Access

My Macbook pro was set up with 2 users - Work and Home. Time Machine was installed on a new external HD. and it did a complete back-up and continued with incremental back-ups. A problem started with emails on the home user part which wasn't easily solved so, in consultation with Apple Help, I set up a second Home Users account - transferring most home files to the new user account and the email problem was solved.

A month or so later the Macbook Pro started seizing during a restart and would only restart in Safe Mode. Disc Utility stated there was a problem with the hard disc that it could not repair. so I swapped the failing disc with a new solid state HD (putting the old HD in a Caddie) and, rather than cloning the old setup which had problems, started with a new installation - transferring files across as required and setting up new email accounts - including importing emails etc from the old HD. However when I tried to access the Time Machine from either the new HD or the old HD (in safe mode) I had no success. The reason for trying to access it was to retrieve the address book, bookmarks etc which seem to have been wiped on the old hard disk. Is there a way of accessing the Time Machine from the new set-up or should I reformat the Time Machine disc and start afresh?