Mail clients will not send password

Question

I posted a question in the eMac discussion group, but realize now that I should have posted it here. So I hope I shall be forgiven for posting it again here.
I have three different mail clients: Apple Mail, SeaMonkey, MS Entourage. I recently had some trouble unconnected with mail that necessitated my switching my computer off by its power switch. Thereafter none of the three mail clients would download mail, all saying that sending my password did not succeed.
The password itself is correct. The e-mail system of my ISP (www.btinternet.com) is web-based, and I have no problem displaying my incoming mail in any of my browsers (Safari, SeaMonkey, Firefox), so this shows that my password is accepted by my ISP.
I therefore did the following: I ran DiskWarrior to rebuild the hard disk directory; I used Onyx to check the S.M.A.R.T. status, to correct permissions and to reset the LaunchServices database; I reset the PRAM.
None of these actions solved the problem. Finally I reset the Open Firmware. Hey presto, this worked.
By an unlucky chance, a few days later there was a brief power cut in my part of town, and once again none of my mail clients would send my password and download mail. So I went through all the above procedures again, with the addition that I used Onyx to verify my startup volume before going on to permissions and the LaunchServices database.
This time nothing, not even resetting Open Firmware, has restored my mail clients' downloading capacities.
What can I do now? I should be immensely grateful for any advice.

Answer 1

Yes, I understand (and understood) that, too, Kurt188. But when I referred to being able to read my mail in my browser, I was not referring to logging in manually (by typing my password). When I open my web-mail in my browser, my password is recognized by my ISP automatically. This must be achieved by software in my computer; otherwise anyone who knows my e-mail address would be able to read my mail without using a password just by going to btinternet.com. Thus my password must be stored in my computer and automatically sent to btinternet every time I go to my mail page on btinternet. That, surely, is a similar process to my mail client sending my password to btinternet.
Admittedly, the password that my mail client sends is stored somewhere associated with that mail client, because when I set up my account in the mail client I had to type my password into the account-setting page (and I had to do the same with each of my backup mail clients). To that extent it is a different process. But the point is that both the web-mail (browser) process and the mail-client process originate in my computer, and both terminate in my ISP recognizing my password (or not!).
The only thing I can think of to account for my problem other than a fault in my software is the supposition that my browsers encode my password differently (perhaps by their particular kinds of encryption) than my mail clients, and that my ISP temporarily recognized all the three browsers' encodings but not the encodings created by each of my three mail clients. It doesn't sound likely to me; but if this is what you meant, I am prepared to bow to superior knowledge and accept your explanation.