Ok, since your internet connection is too slow to download Firefox and you've already tried resetting Safari, let's try resetting Safari's preferences. To do that,
1) Quit Safari.
2) Open a Finder window by clicking the smiling face icon in the lower left of the Dock.
3) Click on your Home folder in the left sidebar.
4) Open the Library folder.
5) Open the Preferences folder.
6) Locate the file named com.apple.safari.plist and throw it in the trash.
7) Close the Finder window.
8) Open Safari and see if it runs faster now.
If that doesn't help much, put additional DNS numbers in from OpenDNS.com. To do that:
1) Open System Preferences and click on Network
2) Click the Advanced button.
3) Click the DNS tab near the top of the window.
4) Click the Plus button near the lower left corner.
5) Add these numbers. Click the plus button once to add the first set, click it again to add the second set:
This information comes from here:
6) Click the Ok button.
7) Click the TCP/IP tab near the upper right corner and click the Renew DHCP Lease button.
8) Once back at the main Network window, click the just over the lock icon and click Set Service Order.
9) Drag the method you are using to connect to the internet to the top.
10) Click Ok
11) Click Apply in the lower right corner.
See how Safari runs now.
If things aren't speeding up yet, create a new user account in System Preferences/Accounts. Quit all applications in your current user account, log out of the current account, login to the new account and surf around with Safari and see if it's faster in the new account.
Let us know how things go after this.
There are more things to try if this doesn't get things going good.