It seems impossible to access my Twitter account. Can you help?

My PC has just been reconfigured (it was terminally ill). Now I can't access Twitter and it is behaving so oddly that I don't know where to start. When I go to www.twitter.com, I get a login page. I entered my details - but nothing happens. When I delete the password and click 'forgotten password' (just in case) it tells me I'm logged in and must first log out - but there is no way on the screen to do this. Lower down the screen there's a line of small writing saying "About Help Blog Status" etc If I click on 'Help', or anything else for that matter, it goes to a screen saying "Unauthorized!" and nothing I do can get me out of that screen. I've tried disabling add-ons (I'm working in Firefox), which doesn't help. I just can't think what else to do.

It doesn't help that the PC is networked to the laptop so now I have the same thing there. I can access Twitter on my iPhone but really want it back on PC and laptop.