Help! How do I get all my mail back?

Question

Basically I just went through **** in a handbasket, trying to transfer my email accounts from one webhost to another -- from Globat to GoDaddy, if the names can help.
Well, I'm still waiting for my accounts to come online -- but I've discovered something truly disturbing: I eliminated the accounts from my Mail program, in order to enter all the new server info -- POP info, new passwords etc.
But now I find that with the elimination of the old accounts, also went everything in their inbox/outboxes! That means I somehow just lost about 1,000 emails that I have received for two accounts, and also the ones that I sent from those two accounts! They just don't exist any more, so that means I've lost all my correspondences, email addreses -- everything for at least the past year.
HOWEVER, I did a backup onto my Time Capsule of this whole computer (MacBook Pro mid 2012) about 6 days ago, and when I go into Time Capsule, there they are -- all those messages, in both my inboxes and outboxes.
However, when I click "Restore," it says "Restoring 987 messages" in my present inbox, but then when it's finished so-called "restoring" them, the inboxes are the same as they were before -- empty.
Now all those messages are on my Time Capsule -- yet when I'm IN Time Machine it won't let me do anything with the messages. Yet it also will not restore them to my present inboxes.
They exist -- on the Time Capsule. But how do I either get them back into my Mail program of now, or somehow save all of them another way in a form that at least will preserve their contents, plus all the addresses etc. etc.?
I don't know how to download them from my old webhost's server, and even if I could, those messages only go back a couple of months and are mixed up with a ton of junk mail. Very soon, my old webhost (Globat) is going to be terminating my account, so they won't exist on Globat's servers either.
How do I get those messages from my Time Capsule to my laptop? I don't mind if they're just one long text file -- I just need them for all the email addresses they contain, and there are some that have personal significance as well. Isn' there a way I can import them all into a new folder in Mail, called, maybe, "Old emails" or something like that?
Help! I didn't even consider this when I went to change webhosts . . .

Answer 1

Okay, here is the deal:
1) I open the "Mail/inbox" for my mail account. Since all the emails aren't there any more, I now click on "Enter Time Machine."
2) Now I select the last date that I backed up my Mac.
3) All the emails that WERE in my inbox on that date show up in Time Machine.
4) I click on "Restore."
5) It says "Restoring 987 files" (all the emails that WERE in my inbox on Dec.6th and which I want to get back)
6) My present day inbox reappears and none of the "Restored" emails are there.
Question: at which point do I Control-click  on all the emails? While they are showing in my Time Machine inbox? (That does not work -- nothing I do does anything -- I just get the error alert sound).
7) when I click on "Restore" it again says "Restoring 987 files," I am back in my present-day inbox and nothing has been restored.
So exactly at which point to I control-click? Do I select all my previous inbox items while in Time Machine and control click? If I do that, nothing happens at all. And if I move back out of Time Machine, nothing has been restored.