Here are the rewritten sentences maintaining the original meanings:

1. Although I was very tired, I didn’t sleep.
=> In spite of being very tired, I didn’t sleep.

2. Although I was hungry, I didn’t eat anything.
=> In spite of being hungry, I didn’t eat anything.

3. Although he felt unwell, he went on working.
=> In spite of feeling unwell, he went on working.

4. Although he was disappointed, he tried to smile.
=> In spite of his disappointment, he tried to smile.

5. He still goes to school although he isn’t fine.
=> In spite of not feeling fine, he still goes to school.

6. Although the salary was low, he accepted the job.
=> Despite the low salary, he accepted the job.

7. In spite of their quarrel, they remain the best of friends.
=> Though they quarreled, they remain the best of friends.

8. In spite of the bad weather, they went out for dinner.
=> Although the weather was bad, they went out for dinner.

9. In spite of his age, he still leads an active life.
=> Even though he is old, he still leads an active life.

10. In spite of his hard work, Ba failed his exam.
=> Though he worked hard, Ba failed his exam.

11. In spite of the heavy rain, we decided to go to see the match.
=> Although it was raining heavily, we decided to go to see the match.

12. Although they lost, the home team played very well.
=> Despite losing, the home team played very well.