Can iPhone storage be read without the 4-digit password? Or is it encrypted? I had a problem with the digitizer connector in my iPhone 5S so I can't use the screen anymore, I couldn't even unlock it to back it up.

So I send it to a logic board specialist to replace damaged connectors with new ones.

My iPhone is locked with a 4 digit password.

Is the data inside its storage accessible somehow without having the 4-digit password? like putting the storage in another logic board or connecting the storage to a computer using special devices and extract data.

Or is it encrypted and can be read only using the 4-digit password?

My iPhone is an 5S with iOS 8.3
Data on an iPhone is always encrypted.  To answer your question it helps to  understand a few things about encryption on the iPhone.  Your data is not actually encrypted with your passcode.  Each file is encrypted with a key.  Those keys are encrypted by other keys in several layers.  These layers enable granular control over which applications and processes on the phone can access the data.  Each of these keys are "strong" (meaning it is really long) and cannot be easily guessed.  At the final level the keys are encrypted using a combination of two pieces of information.  The first piece of information is tied to the hardware and is "strong" so it is not practical to try and guess it.  The second is your passcode.  A four digit passcode is considered weak and can be cracked in a matter of minutes if the person trying to break in can make a large number of attempts.  If someone has access to all your hardware then it would be possible to read your data.  If you have set your phone to wipe after 10 bad password attempts then it is harder.  However, it turns out that most people pick a passcode that can easily be guessed in less then 10 attempts.  You might be surprised how many phones can be unlocked with "1234".  If the person trying to get your data doesn't have your phone (e.g. they insert your storage into a different device) then it is virtually impossible to read your data.

In summary, if you have selected a passcode that is not easy to guess and set your phone to wipe after 10 bad password attempts then your data is safe, otherwise you might have cause to worry.