Hello, I'm Tim and will do my best to help you today.
What OS are you using? Windows or MAC ? When did it last work? What happens when you try and open it, nothing, and error?
interesting, so too much mail has stacked up probably....
How much mail is there? and is there any that can be deleted?
Your smart phone is probably reading the emails off of the server, your Thunderbird client is downloading them...
6000 is a fair amount but not crazy unless they have alot of attachments. I'm sure you saw this article
I can remote in and see what I can do, if i can get them compressed or if we can switch it to just view mail on the server, like your phone.