The ISP shouldn't know how your email is sent
Whilst I don't use Thunderbird, many other do with no problems, what is your ISP ?
Perhaps we have others using that ISP
I have done a google search for part of your error message 'Server response 421 connect error 10053' without the quotes and it returns many hits, it may take some finding for something directly relating to your set-up.
http://www.4d.fr/documentation/4Ddoc2003/CMU/CMU88906.HTM SMTP 421 - Service not available, closing transmission channel.
This sounds like a server problem.
A google search for 'error number 0x800ccc67' also returns many hits. This one is basically the same from 2004,
http://www.mcse.ms/archive170-2004-6-813365.html and this which is OE and Tbird
http://www.ureader.co.uk/message/627213.aspx.
Does your server require authentication, have you got that option ticked, etc. ?
Are you trying to send SSL email using the SMTP port 25 ?
I'm out of ideas, I haven't come across anything like this before were email can be received but not sent, even with two email programs.