Sure, here are the verbs in the sentences correctly conjugated:

1. When the painter felt the ladder **beginning** to **slip**, he grabbed the gutter to **save** himself from **falling**.
2. The snow kept **falling** and the workmen grew tired of **trying** to **keep** the roads clear.
3. He offered to **lend** me the money. I didn’t like **taking** it but I had no alternative.
4. What was in the letter? I don’t know. I didn’t like **opening** it as it wasn’t addressed to me.
5. Do you remember **hearing** the bombs **dropping**? No, in the last war I was too young to **realize** what was happening.
6. Did you remember to **book** seats for the theatre tomorrow? Yes, I have the tickets here. Would you like to **keep** them? I am inclined to **lose** theatre tickets.
7. Try to **avoid** **being** late. He hates **being** kept **waiting**.
8. I didn’t know how to **get** to your house so I stopped to **ask** the way.
9. I wish my refrigerator would stop **making** that horrible noise. You can’t hear anyone **speak**.
10. This book tells you how to **win** at games without actually **cheating**.
11. The enemy began **firing**. He felt bullets **striking** the wall behind him.
12. You don’t need to **ask** his permission every time you want to **leave** the room.
13. The police accused him of **setting** fire to the building but he denied **having been** in the area on the night of the fire.
14. I left my door open. Why didn’t you walk in? I didn’t like **going** in when you weren’t there.
15. It’s much better to **go** to a hairdresser than to **try** to **save** time by **cutting** your own hair.
16. I’d rather **earn** my living by **scrubbing** floors than **make** money by **blackmailing** people.
17. Did you remember to **lock** the door? No, I didn’t. I’d better **go** back and **do** it now.
18. You still have a lot to **learn** if you’ll forgive my **saying** so.
19. It’s no use **trying** to **interrupt** him. You’ll have to **wait** till he stops **talking**.
20. I’m for **doing** nothing till the police arrive. They don’t like you **moving** anything when a crime has been committed.
21. He didn’t like **leaving** the children alone in the house but he had no alternative as he had to **go** out to work.
22. Why didn’t you drink it? I didn’t like **drinking** it as I didn’t know what it was.
23. I’m very sorry for **being** late. It was good of you to **wait** for me.
24. I keep **trying** to **make** mayonnaise but I never succeed. Try **adding** the yolk of a hard-boiled egg.
25. Do you feel like **going** to a film or would you rather **stay** at home?
26. She told me to **look** through her correspondence and **take** out any letters that you had written her. I didn’t like **looking** through someone else’s letters but I had to **do** as she said.
27. He took to **getting up** early and **walking** noisily about the house.
28. I liked **listening** to folk music much better than **listening** to pop.
29. The car began **making** an extraordinary noise so I stopped to **see** what it was.
30. You’ll never regret **doing** a kind action.
31. He decided to **put** broken glass on top of his wall to **prevent** boys from **climbing** over it.
32. He annoyed me very much by **taking** the piece of cake that I was keeping to **eat** after my supper.
33. He kept **ringing** up and **asking** for an explanation and she didn’t know what to **do** about him.
34. We got tired of **waiting** for the weather to **clear** and finally decided to **set** out in the rain.
35. He made me **repeat** his instructions to **make** sure that I understood what I was to **do** after he had gone.
36. I suggest **leaving** the car here and **sending** a breakdown van to **tow** it to the garage.