iPhone not restoring (errors) and stuck in recovery mode, after strange sim-card behaviour

Phone: iPhone 5S

OS: iOS 8.4

(Unfortunately no other details can be provided at this stage as phone is stuck in recovery mode)

Hi. I have an iPhone 5S which is currently stuck in recovery mode and will not restore or update. This occurred after its sim-card functions started acting strangely.

We know that when a sim-card is installed, the status bar will display "Searching", and either show your carrier name with signal strength or No Signal / SOS Only. When you do not sim-card installed, the status bar will simply say No Sim, and in fact you get an alert in the lock screen saying no sim is installed.

MY phone however, fails ALL of that. Instead, the status bar where those things should be, displays the Apple Logo followed by iPhone. I did NOT jailbreak, therefore it is NOT a custom carrier logo. The characters displayed do not change when I remove the sim card.

Things I have tried (all without fix)

1. Reboot

2. Turn off device, remove sim card, reboot. Status bar does NOT display No Sim, as it still displays "logo+iPhone"

3. Turn off device, remove sim card and put it back, reboot. No luck

4. Took sim card to an old iPhone, which worked - therefore the sim card has no problem.

This is also not a display bug as I cannot make calls or send texts.

Facing this strange behaviour, I thought of the only option: restore my phone. So I plugged my phone in and clicked Update, hoping iOS 9 would install. Update seems to run fine at first, it extracts the software, verifies it, installs, verifies the installation then begins a firmware update at which point it errors saying 'The iPhone "iPhone" could not be restored. An unknown error occurred (1).' After re-trying 5 times, I ended up with errors 14 and 40 once each, and 1 for the rest. So I thought, the phone must have to be restored to factory settings then. So I put the device into recovery mode and tried again with no luck. And now it is stuck in recovery mode. I've tried uninstalling iTunes and re-download the latest version on Apple's official website. No luck there.

Using a 3rd party recovery tool which can help devices exit recovery mode, my phone did exit recovery mode. But now it won't turn on. The screen flashes on and the apple logo is displayed as per usual. This lasts for 5-8 seconds and the device turns off. It does NOT repeat the process itself, it is not stuck in a loop. So now I believe my device is in the state of being off. I can still enter Recovery Mode as I have tried. I can not find any information on error 1, except that it may be a hardware problem.

So, TLDR: iPhone 5S Running iOS 8.4 displays apple logo upon boot and turns off, and remains off, it does not loop. It will NOT Update or Restore with unknown errors 1, 14 and 40, and cannot exit recovery mode.

This is my first time on support community, sorry if I have missed any details and if my descriptions are not clear.

Thanks in advance.