In diagnosing this myself, if you are saying you cannot always logon to the router, then it still sounds to me like the wireless is dropping out.
If we start at the beginning, your other laptop works fine, I presume via wireless.
This rules out everything from the Internet connection all the way up to the router (but not including the router).
So, on the duff laptop, I would open up another cmd (START > RUN > 'CMD' > [OK]).
Then type ipconfig and look for the Default Gateway. With the router you have, it should be 192.168.0.1.
Whatever the Default Gateway is, type in the following command and leave it running and then use the laptop as you were:
ping -t 0.0.0.0
(where 0.0.0.0 is the Default Gagteway e.g. ping -t 192.168.0.1)
Then see what happens. You should get something like this repeating down the page:
Reply from 192.168.0.1: bytes=32 time=1ms TTL=255
If not, wait for a while until you do as it could have dropped out at that moment.
Once you get the reply from, then carry on using the Internet as normal.
If you notice it stops working, have a look and see what the ping window is doing.
If it is not saying 'Reply from 192.168.0.1: bytes=32 time=1ms TTL=255', it might be saying:
Request Timed Out
If so, wait and see what happens. The reply should return and then it should be working again.
I am still in the 90's% certain it is your drivers, except that if a rollback to a previous version did not work, you need to find even more up to date drivers than those you were running when you first had the issue.
This might mean going to the laptop vendor or even the WiFi adapter manufacturer (e.g. Intel).
It could be the chipset in the router but I have the same router and have yet to find a WiFi adapter which doesn't work.
You can turn off wireless and plug in with a network cable to see if you get any outage as suggested. If not, you know you are most likely dealing with a wireless adapter or router wireless issue.
PS: No, you do not want WPA turned off, and ideally you want to use WPA2.