Hello.

This kind of issues are, unfortunately, more common and the we'd like. Thankfully, 99% of the cases are very easy to solve. However, you do need to diagnose what your exact problem is. Do this:

1. run Firefox in safe-mode to disable all extensions and plugins. If this fixes your issues, be them with RAM or CPU usage, then you know it's a problem with plugins or extensions. Proceed to number 2. If safe-mode doesn't fix the issues, then read bellow, after this list;
2. update all extensions and plugins in your Firefox. If this doesn't solve the issues, proceed to the following number;
3. disable all extensions and plugins in your Firefox (not running safe-mode). Being certain that, as in safe-mode, the problems you're having have gone away, enable one plugin at a time. You should be certain that you WANT that plugin to be enabled, so keep your overall number of plugins as low as possible. When you encounter the problems, you know you've found a problematic plugin, so disable it for good. Keep enabling all plugins (except problematic ones) until you've gone through them all.
4. enable one extension at a time. Again, be certain that you WANT that extension to be enabled, so keep your overall number of extensions as low as possible. When you encounter the problems, you know you've found a problematic extension, so disable it for good. Keep enabling all your extensions (except problematic ones) until you've gone through them all;
5. you're done! You've fixed your problems with problematic add-ons.

Ok, if disabling all extensions and plugins through safe-mode didn't work to bring Firefox's CPU and RAM usage to good levels, then you have different issue. The most likely scenario is that you have a third party software running on your computer that is messing with Firefox. Do as follows:

1. do a virus/malware check on your computer. If this doesn't fix it, proceed;
2. disable all software running in the background that you don't want to have running in the background (in windows, this is done by pressing WINDOWS+R in your keyboard, typing "msconfig" (without the commas) and pressing enter. Now, under the "Startup" tab, you can uncheck the software you don't want, and reboot your system for changes to take effect. If you're unsure of what software you want running, ask someone with more experience). If this doesn't fix your issues with Firefox, proceed;
3. check your firewall/antivirus/security suite for enabled functions/features that you don't want and/or may be conflicting with Firefox. You'll find that these features are most likely tied to Internet Security features, such as link scanners or URL checkers and the like. If you're not sure they are conflicting with Firefox, simply try to disable them to see whether or not that's true. As long as you don't browse the web with your antivirus completely off and your firewall completely turned off, there should be no problems. If this doesn't solve the issues, proceed to the following number;
4. check your operating system security options, mainly advanced options that are not configured by default. While it's very unlikely that this may be the cause of the problem (after all, it's the last item on the list), it's remotely possible. If this doesn't work, proceed to the following point;
5. clean up your OS registry, using appropriate software. If this doesn't do it, I'm out of ideas. Except make sure you've followed my instructions correctly.

Hopefully my tests here might contribute towards finding a solution to this problem:

I installed a NEW version of firefox portable 7.0.1 - completely empty- and tested with it. (I followed a document I found on dhdaily.com on how to install it in parallel.)

I made the following discovery: Firefox runs normally IF you only open up one tab. If you open up more than one tab at a time, EACH TAB must complete IN ORDER before the next one works. So site 1 has to load to completion before site 2 can complete etc. If any site is slow, then the rest of the chain is slow.

As a test, I opened up my EBAY account and, while it was loading, opened up my feedback in a second tab. The second tab would not even start until the first tab page completed.

I then closed and restarted Firefox and opened up three different webpages in three tabs: www.google.com www.refdesk.com www.microsoft.com. Again google had to finish before refdesk would load. Refdesk, being large, stopped Microsoft from completely loading until it finished.

So it seems to be some sort of thread balancing issue involved where the first tab is not playing well with subsequent ones.

Ok, I found the solution (for at least my boxes!) Yay!

The trouble is that Firefox changed the amount of HTTP connections it permits simultaneously from 30 (pre version 6) up to 256 for version 7. Each connection uses CPU and Memory!!!!!

I won't ponder why they did that, but the fix is easy:

Lower the max number of HTTP connections

 In the Location bar, type about:config and press Enter.
     The about:config "This might void your warranty!" warning page may appear. Click I'll be careful, I promise!, to continue to the about:config page. 
 In the Filter box at the top, type network.http.max-connections.
 Double-click on the network.http.max-connections preference, the "Enter integer value" dialog box will open.
 In the field, type 30 which was the default value in old versions of Firefox and click OK.

My version 7.0.1 firefox suddenly started working! Yay!