David Perry wrote:
I have had to rebuild my computer.
So I was going to use the migration assistant to recover all my data apps etc from my time machine backups.
However Migration assistant would not recognise my time machine disk.
I built a basic system and then used time machine to use the disk, which it did.
It also created a new backup for me.
There's the rub: Migration Assistant (and Setup Assistant) use only the most recent backup; you don't get the choice to use an earlier one.
Ordinarily, your best bet is to do a full system restore, per #14 in [Time Machine - Frequently Asked Questions|http://web.me.com/pondini/Time_Machine/FAQ.html] (or use the link in *User Tips* at the top of this forum). There you do get a choice, but it starts by erasing your disk, so you lose everything you put on it.
Without knowing why the disk wasn't recognized, it's hard to be sure, but I'd recommend Repairing the backup disk, per #A5 in [Time Machine - Troubleshooting|http://web.me.com/pondini/Time_Machine/Troubleshooting.html] (or use the link in *User Tips* at the top of this forum).
If that either finds no problems, or fixes any it does find, starting over with a full restore might be best. If at first you don't see the backups you want in step (g) there, click the "pop-up" menu; there are probably two versions of your Startup drive shown there.
Depending on why you had to "rebuild" your computer, whatever was wrong may have corrupted some things on your internal HD, and Time Machine may have backed-up the damage, so the restored system may not start, or may kernel panic, or not work well. If that happens, try again, but select an earlier backup, before the problems started.
If there are things you put on your disk after the rebuild that you need to recover, you should be able to do selective restores from the later backups, via the "Star Wars" display. See #15 in the FAQ.
One advantage to starting over is that the user accounts will be recognized as the same ones as on your backups. That may not be the case with Migration Assistant, and you may lose permission to files on other disks, including your backups.
But if you can't or don't want to start over, you should be able to at least view the earlier backups, via the +*Browse ...+* option, per #17 in the FAQ. You may or may not have permission to restore from them.