Possibly infected machine - Please help

I have noticed strange and worrying behavior of my computer recently and suspect it might be infected.

It appears that something in the computer is blocking certain websites/pages which are security related.

I will explain everything in detail.

I have Windows XP, SP3 and NIS 2009.

It started with me not being able to open Norton Safe Web website.
 At first I thought that the website might be down and did not worry about it too much. However after several days I posted a question on these forums and was told that the website is working fine.

I received several advices which I tried , unsuccessfully
I was also advised to update my NIS 2009 to NIS 2010.

I tried to do that by going to Norton Update Center. However when I clicked on Norton Product Updates link - I could not connect to that page. I got Network Timeout message.

That was the first warning bell as I tried it in 3 different browsers and in the past I could connect to it without a problem, but not anymore.

 

Then I tried to go to www.norton.com/nis10 to download NIS 2010, but got the Network Timeout message as well.

 

I ran a full system scan with NIS 2009 in safe mode with networking - nothing.

About 2 years ago I installed Malwarebytes on my computer. I have not used it since.
So I tried to update it in order to run a scan, but was not able to do so.
I got a message: Update failed. Make sure you are connected to the internet and your firewall is set to allow Malwarebytes Anti Malware to access the internet.
That was the second bell because I don't think here is anything wrong with the firewall .

 I tried to download  the latest version of Malwarebytes, but I was not able to connect to the Malwarebytes website www.malwarebytes.org/
Then I tried the Malwarebytes download link at  download.cnet.com/Malwarebytes.../3000-8022_4-10804572.html, but was not able to open that page either.

Finally I managed to download the latest Malwarebytes version installer from FileHippo.com.
It is currently on my desktop.
I am not sure if I should try and install it over the old version or not. Or maybe do something else.

My restore points also appear to be gone, so I could not go back to before the problems started.

 

I am not really computer savvy but all this seems very strange to me.

Any help would be greatly appreciated.

 

Thank you, Alex.