I hope you don't mind.
I agree with the poster malwfix below about add-ons, but back to that in a minute.
All these are for Firefox unless I state otherwise.
1] Can I just check that the site you are having problems with is http://www.malwarebytes.org/ ?
I ask because further up the thread you said malwarebyte.org (no "s" on the end of malwarebyte). I tried that and got redirected to some web site that my Firefox security add-on WOT, (Web of Trust), warned me not to go further.
I can get to http://www.malwarebytes.org/ without any problems
2] I was going to ask you to check the "Ping" for www.malwarebytes.org but I am getting some strange results myself.
Ping is a single packet of data sent through the computer's "Command Prompt", (Start > All programs > Accessories > Command Prompt), by typing ping www.malwarebytes.org then pressing enter. Note the space after ping. To exit the Command Prompt, type in exit and press Enter.
This sends one packet of data and traces the route it takes. Normally if ping wasn't working, the results would show a failure, but my ping works. Ping also shows the IP address for www.malwarebytes.org .
The problem I had was, when I wrote down this IP address then entered that into the browser address bar, I got a browser error saying 404 Not Found.
That said, some web sites disable ping or redirect it to protect against hacker attacks or Denial of Service attacks. So I see no benefit in asking you to try ping.
3] What does your search engine do if you type in Malwarebytes?
First of all, type www.google.com into your address bar and press Enter. In the Google search box type in Malwarebytes and click Enter.
What entries do you see? The first link should be for www.malwarebytes.org , (the green font entry under the link). If so, click the link and tell us what happens. Do the same in Chrome and IE and compare the differences.
4] Back to malwfix's suggestion, I think you should try it for Firefox, although I am unsure why it should solve the issue for FF when Chrome still has a problem.
But any way, open Firefox in it's Safe Mode. I don't know what OS you are running nor what version of Firefox, but if the FF version is recent, click the Firefox tab top left, goto Help then select "Restart with Add-ons Disabled...".
This will restart Firefox with the options shown here; http://support.mozilla.org/en-US/kb/Safe%20Mode
Do not tick any options but instead click the "Continue in Safe Mode" button. Now see if the link above and/or www.malwarebytes.org works for you.
If so, then either one of your FF add-ons is causing problems, or your selected search engine is redirecting you. Restart FF in it's Safe Mode, and in the options, disable all add-ons, reset toolbars, and set default search engines. You can add back in the add-ons one at a time.
5] Tell us how you get on.