I suspect you have only one SMTP server set up in Thunderbird, and it's trying to send mail via ISP2 when you're connected to ISP1.
Click on the name of the account that cannot send (in the LH margin), then on "View Settings for this Account". Scroll right down to the bottom of the LEFT HAND window that appears, where you'll see "Outgoing Server (SMTP)". (NOT the box in the RH window).
If there's only one there, then you need to add another, with the SMTP server name for the other ISP.
Then, go back to the "View Settings for this Account" page, and look in the box "Outgoing Server (SMTP)" in the right hand half of the page. Change that to the correct one, and banzai.