Ok last try before I go for the TeamViewer option:
There are actually what appears to be 3 'root' users with a default out of the box install of wamp.
root@localhost
root@127.0.0.1root@::1
These indicate that you can login with the root password from 3 different ip address's.
When you add a password to the root user do you add it ( the same one ) to all 3 or just one of these?
They are all basically the same place but are actually different and depend upon setup and which IP Address range the browser uses ( arbitrary decision in some cases ).
If you change the root@localhost password but the browser uses the IPV6 ::1 address and you have not setup your hosts file so it knows that ::1 is also called localhost this could explain your problem.
So basically add the same password OR remove the password from all 3 and see what happens.