Earlier today, I turned on my laptop on. Earlier today, I turned on my laptop.

Everything was fine, until I plugged int in to charginge. Everything was fine, until I plugged it in to charge.

I hope this is what you were trying to say? You didn't have any adjective in there, so I put "everything was fine". Instead of saying "I plugged it in charging", you say either "I plugged it in," "I plugged it in to charge," or "I started charging it."

Everything was okay until I plugged it in to charginge. Everything was okay until I plugged it in to charge.

It’sOn the screen appeared, something strange appeared. On the screen, something strange appeared.

You use the preposition "on" when talking about screens/phones/computers etc ... anything *on* the screen is something you can see.

It’On its screen appeared something strange. On its screen appeared something strange.

I don’t know what is it.t was, I don’t know what it was,

I don’t know what ist its. I don’t know what it is.

Bbut Iit looked likes a lot of white lines running along the screen. but it looked like a lot of white lines running along the screen.

You can combine these two sentences :)

But It looks likes a lot of white lines running along the screen. But It looks like a lot of white lines running along the screen.

It covers all laptop’sed the entire screen. It covered the entire screen.

You used the possessive ('s) right, but you wouldn't use it here. You can either just say "laptop screen" or "screen". It sounds more natural to say screen.

It covers all of the laptop’s screen. It covers all of the laptop’s screen.

I can’t see anything, so I can’t do anything on my laptop. I can’t see anything, so I can’t do anything on my laptop.

I tried restarting my laptop., I tried restarting my laptop,

Bbut this wayrestarting didn’'t workdo anything to fix the problem. but restarting didn't do anything to fix the problem.

Sounds better like this.

I will replace new laptop’sthe screen next week. I will replace the screen next week.

When you say replace, you don't need to say new, because replacing something already means you will get something new.

I will replace newthe laptop’s screen with a new one next week. I will replace the laptop’s screen with a new one next week.