Unfortunately, we have no way to help if you don't provide more details. Are you using an email client (Outlook, Thunderbird, etc.)? Or are you using a webmail service? And which one: Gmail, Outlook, AOL, etc.?
Also, is there trash already in the Trash folder? If so, have you tried emptying that folder first (permanently deleting contents) and then tried moving messages there? (Some services, like Hushmail, I believe, have a small free storage and won't allow messages to be moved to the trash if it will exceed certain limits.) Or is your trash folder already empty or mostly empty)?
Hmm... I'm afraid I'm at a loss here. I've never encountered this. We'll have to wait to see if Ray (popowich) can help. In the meantime, it still would help knowing exactly which service is giving you this trouble (Gmail, Yahoo, etc.).
And just for clarification: Since you're obviously able to log in, are you able to do anything at all, like read new emails or compose emails? If you send an email to this account from another one, will it show up in the inbox the next time you log in? Can you do anything in the settings like change a theme? Or is everything at a complete standstill after logging in (including inbox not showing recently received emails?
Have you tried submitting a support ticket with the service or ask in its own help forums to see if others have experienced this?