The electricity failed.

Correction: The electricity went out.

[We use out instead of fail, or off. If you wanted to say that it failed, you would say the POWER failed. For some reason, we make this distinction].

3 days ago,it was heavy rain with thunder and lightning.
Lightning struck a telegraph pole in front of my house.
And then, the electricity was off for 6 hours in my house.

Correction: Three days ago, there was a thunderstorm. Lightning struck a a telephone pole in front of my house, which shut the electricity off for 6 hours.

[Rain + Lightning + Thunder = Thunderstorm. We refer to these poles as telephone poles. Also, when you talk about an event (Lightning struck a telephone pole), that event caused something (shutting your electricity off), and they belong in the same sentence.]

By the way, this time I thought how important the electricity is.
And when I think back on what I did, I feel pretty stupid.

Correction: By the way, at this time I thought about how important the electricity was, and when I think about what I did, I feel pretty stupid.

[Remember, in English we make heavy distinctions about how you make reflections (I thought, thinking back, etc.), you always want to say "about", or give a very specific subject. Also, remember that the verb tense is very important.]

When I didn't have the electricity, there were too many things I could not do.
- I could not cook and take a bath because It's controled by the electricity.
- I could not watch TV or Internet news so I could not know what's happened.
- I could not work because I am a system engineer.
- I could not use an air conditioner. (The temperature was 34 degrees)
- I could not use my cell phone.(Unfortunately, the charge was almost 0%)

etc....

Correction:

When I didn't have electricity, there were so many things I could not do, such as:

- I could not cook or take a bath because they are controlled by electricity.

- I could watch TV or the internet news, so I did not know what was happening.

- I could not work because I am a system engineer.

- I could not use an air conditioner. (The temperature was 34 degrees).

- I could not use my cell phone. (Unfortunately, the battery was almost dead).

[Instead of etc, you can use "such as" with a colon (:) to let people know that the list isn't complete. Otherwise, this section was really well done.]

In summary, I could not do anything.
I was only just panicking with my cat.

Correction: In summary, I could not do anything. All I could do was panic with my cat.

[The last sentence should make a reference to the previous sentence. You couldn't do anything, but you were panicking with your cat? You need to say along the lines of "I couldn't do anything, BUT..."]

I thought I have to know how to get over a crisis more...

Correction: It made me think about how I have to know about how to get over a crisis.

[This sentence should reference your previous story. What made you think about how to get over a crisis? This crisis.]

I hope this helps! Having no electricity can be terrible! I have had the same thing happen to me, but fortunately everything that batteries was still fully charged. I, too, hope you will be more prepared next time!

:D