Could the brand new router be the problem? Go to starbucks or mcdondalds or a friend's house with wifi to test out. I have seen some wifi complaints even before ICS and it may be because Android can be finicky with certain routers.
I am still on Honeycomb and have not been prompted to upgrade. My tab wifi works great and would be reluctant to upgrade if this turns out to be a problem. I had similar problem when I upgraded my phone from 2.1 to 2.3 (subsequently fixed by LG) and it caused a lot of grief.