Weird internet problem / ssl connection error, site loads in safari not in firefox or other way around

Question

I really can't figure out this problem. Search the internet tried all kinds of things, nothing help so far.
I have a Macbook Pro (Lion originally installed) running on Mavericks (all latest updates). SSD installed and the DVD tray is replaced by the original HDD.
The laptop wasn't running very smooth anymore so decided to give it a fresh Mavericks install (even though I know it's not really necessary for mac, it helped, everything is much faster except a weird internet problem came up).
After freshly installing Mavericks I couldn't get into my google account anymore, just wouldn't load. Tried Safari (use this normally) and Firefox and Chrome, this last was gave a SSL connection error, both Safari and FF said the website couldn't be loaded because the server didn't respond. For Gmail I use Mailplane which is just stuck on a white page. I tried repairing the keychain, repaired disk and disk permissions, cleaned browsers, turned off firewall and antivirus (Shopos) started in safe mode, checked time settings which were all good. Nothing of this helped. I even ended up creating a usb bootdisk for Mavericks, formatted the disk and reinstalled from the start just Mavericks and nothing else, started Safari, still the same problem. As even this didn't help I figured it's not worth reinstalling all software so put back my backup.
Now I ended up somehow only being able to use Gmail normally in Firefox, Chrome still gives SSL error and Safari can load the inbox, but I can't open any messages. I get the error there is a problem with the connection. If I try in Basic HTML mode it surprisingly does work.
You would say, just use Firefox, finished...but the thing is that sometimes random websites won't load in Firefox, when I load the same site in Safari it works perfectly.
O yes, I also tried the connect to my iPhone and use the Cellular data network, then it's no problem using Gmail in Safari normally. You would say it's a router problem, but I have another Macbook Pro (just one model later running Mountain Lion) this one works perfectly with every browser. Also my iPhone does everyting logged into the WiFi network.
You can understand I really have no clue what's going on here, I don't see any logic. I can only think of a hardware problem in my Macbook, but don't see how that could cause these problems.
I hope someone is ably to help me ?

Answer 1

Please read this whole message before doing anything.
This procedure is a test, not a solution. Don’t be disappointed when you find that nothing has changed after you complete it.
Step 1
The purpose of this step is to determine whether the problem is localized to your user account.
Enable guest logins* and log in as Guest. Don't use the Safari-only “Guest User” login created by “Find My Mac.”
While logged in as Guest, you won’t have access to any of your documents or settings. Applications will behave as if you were running them for the first time. Don’t be alarmed by this behavior; it’s normal. If you need any passwords or other personal data in order to complete the test, memorize, print, or write them down before you begin.
Test while logged in as Guest. Same problem?
After testing, log out of the guest account and, in your own account, disable it if you wish. Any files you created in the guest account will be deleted automatically when you log out of it.
*Note: If you’ve activated “Find My Mac” or FileVault, then you can’t enable the Guest account. The “Guest User” login created by “Find My Mac” is not the same. Create a new account in which to test, and delete it, including its home folder, after testing.
Step 2
The purpose of this step is to determine whether the problem is caused by third-party system modifications that load automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Please take this step regardless of the results of Step 1.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.
Note: If FileVault is enabled, or if a firmware password is set, or if the startup volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.
The login screen appears even if you usually log in automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of Steps 1 and 2.