Have you tried asking on MozillaZine, which does not charge for assisting others? (I'd have posted any relevant KnowledgeBase articles, but that site is being overly slow again today, and you may encounter MozillaZine delays as well.)
Timeouts of the nature you are encountering are usually network problems, not TB-related ones, but it won't hurt to ask in the TB Support forum, which does not require registration, and they may be caused by such things as telling TB to use improper security settings.
(That you also encountered problems in using Windows Live Mail tells me that you do have one or more [or perhaps umpteen gazillion...] setup problems somewhere.)
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