Just an idea. Could you try:
Avast main GUI -> real time shields ->
Script Web Shield -> expert settings -> "Scan traffic from well known browser processes only".
Please save and reboot (in theory, not necessary, but how many times we have seen a simple reboot solves problems?).
Then try again accessing Sky Drive. Of course, if this success, it could also be just a coincidence
.
[EDIT]
Corrected the shield.
[/EDIT]