Let's go through each sentence and identify the underlined part that needs correction:

1. I look forward to have the resolution to the problem I have mentioned.
The correct form should be: "I look forward to having the resolution to the problem I have mentioned."
Correction: A (to have -> having)

2. They have moved nothing in your room while they sent you to the hospital.
The sentence is grammatically correct and doesn't require any correction.

3. Aren't you afraid that they will sack you if you didn't start coming to work on time.
The correct form should be: "Aren't you afraid that they will sack you if you don't start coming to work on time."
Correction: D (didn't start -> don't start)

4. I had to drive to the factory to pick up my brother, who's car couldn't start.
The word "who's" should be corrected to "whose."
Correction: B (who's -> whose)

5. It was not easy for usgetting tickets for the concert.
The correct form should be: "It was not easy for us to get tickets for the concert."
Correction: C (usgetting -> to get)

So, the correct sentences are:
1. I look forward to having the resolution to the problem I have mentioned.
3. Aren't you afraid that they will sack you if you don't start coming to work on time.
4. I had to drive to the factory to pick up my brother, whose car couldn't start.
5. It was not easy for us to get tickets for the concert.