1. Control Panel, Windows Firewall, Exceptions tab, click the Add Program... button. You will see a list of programs, check is ashWebSv.exe is in it (probably not), if not use thw Browse button to navigate to the C:\Program Files\Alwil Software\Avast4 folder and select the ashWebSv.exe.
I somehow doubt that this will resolve the problem, but it eliminates one other thing. The reason I think this is I'm sure that the web shield works with other web pages and if it were somehow blocked by the firewall it should be consistent across all pages.
2 & 3. You will need to look at the Tools, Internet Options, Security tab, and ensure Javascript is enabled (Custom Level button). I think it comes under the heading of Active Scripting, but it really is so long since I used IE.
Either that or try using firefox or opera browser, personally I feel they are more secure anyway.
4. As I feared if it might be NAV related a reinstall would be unlikely to have a effect.
5. You shouldn't turn off avast completely as that disables all protection, but Terminate the Web Shield which is the only element likely to be effected, try that. If that doesn't work then avast isn't the cause but something else, javascript or cookies not enabled possibly. I would also suggest trying a different browser and see if Hotmail works with that.