how to activate iphone4 factory locked without sim carreer?

You don't. A SIM is REQUIRED to activate it. If it's carrier locked, it must be a SIM from the carrier it's locked to.

Then restore the iPhone via iTunes, and with a valid SIM card inserted into the device.

That's probably because it was hacked to unlock it and has now been rendered useless.

Start the process to unlock your iPhone:

1. See if your carrier offers unlocking. Only your carrier can unlock your iPhone.
2. Contact your carrier and request an unlock. You might need to meet requirements to qualify for unlocking. After your carrier submits the unlocking request, it may take up to seven days.
3. After your carrier confirms that your iPhone unlock has been processed, go to the next section.

If you have a SIM card from a different carrier than your current carrier and your current carrier confirmed that your iPhone is unlocked, follow these steps:

1. Remove your SIM card and insert the new SIM card.
2. Complete the setup process.

If you don't have another SIM card you can use, follow these steps to complete the process:

1. Back up your iPhone.
2. Erase your iPhone.
3. Complete the setup assistant and restore your backup.

If you experience issues or see the following message in iTunes or on your device, follow the steps below:"The SIM card inserted in this iPhone does not appear to be supported. Only compatible SIM cards from a supported carrier may be used to activate iPhone. Please insert the SIM card that came with your iPhone or visit a supported carrier store."

1. Restore your iPhone.
2. Contact your carrier to verify that the unlock was applied in your carrier's system.
3. if you are in such a situation that you can't find help legally. you will how to make someone do it for you
4. P.S Obama administration is going to make it legal to unlock your iPhone by end of 2014 you will have to wait for it. you can try waiting for it to happen.