Z61t refuses go to sleep mode

[Diehard]

I have posted in the wrong place. This is the right one! I'm sorry

Hello everyone!

I just bought an used Z61t. Its original OS was XP Pro, but has been ungraded to Vista Ultimate. I have some problem with it now

1) Using Power through AC Adapter, the laptop refuses to sleep when I press Fn+F4 or sleep of Vista. LCD went black, Hard drive off.. Then 1 second later the hard driver's on. LCD's still black but not in sleep mode. If I remove the mouse, the Laptop will ask me password just like screen saver mode.
It never happens when using Battery!

2) I was surfing web. Then, I can not visit other websites than Google (Problem loading page :Server not found error). Even though the Local net is still working. I have to plug it out and in back so I can visit other websites. I'm using Firefox and IE, it happens to both.

Is it normal for Vista if it uses 550 to 600+ MBRam?

Hope you guys can help me out!

Thanks

MOD EDIT: Please do not double post.