First option: Create a TB style back-up and select everything, install TB on your new pc and tell it it restore accounts from your back-up. This has the disadvantage that all of your paths have to be the same on your old and new system.

Second option: Start Regedit on your old pc and export the key "HKEY_CURRENT_USER\Software\RIT\The Bat!" to a file (call it TB.reg)
Now copy both your mail directory and this TB.reg file to your new pc. When you don't place your mail directory to the same path as it was on your old pc, that's no problem, it can be remedied this way.
In order to restore the registry settings, you open the TB.reg file, this will prompt the question whether you want add the contents to the registry and of course you say 'yes'
Now if you're using a different path to your mail directory, just start regedit and adjust the key "HKEY_CURRENT_USER\Software\RIT\The Bat!\Working Directory" to your liking.
Now you install TB and it'll accept the settings.
In case you don't like to play with your registry, you can also forget about that part and only copy your mail directory.
After installing TB you tell it to create new acccounts. Point it to your copied mail directory and tell TB to use accounts with the existing names, TB will take those settings.

I've followed the third procedure.
I have the Mail folder from the old pc.
I've installed TB, copied the Mail folder into its programm path. Then I do this:

Account -> New
Diaglog Box Appear with:
Account Name:
POSTMASTER -> exactly as the folder inside /Mail folder

Root Directory (or similar, I'm running spanish version):
<predefined>, I choose Search and select the same /Mail folder and this keeps <predefined>.

--Next->

Your Full Name: POSTMASTER
Email Aaddrees: the address ... (it does not matter what I put in there, because It should be able to retrieve settings with the account name identical to the Mail/POSTMASTER folder).
Organization: I leave this empty

--Next->
--Next->

Whish to set the rest of options now?: NO

The account appears... empty

I've solved the problem. Deinstalling TB 3.71, installing TB 3.0 that thats no requiere encription.
Added one by one the accounts, that where recognized perfectly, then exporting to TB format backup.

Installing 3.71 and then importing.

It worked.

I promise I'll pay for this app as soon I have money to pay for the electricity bill and the phone, and internet.... and yes... some food.

Thanks a lot, the app is great.