The rainwater drains from the roof of our house through the PVC pipe which is in the wall to the water tank below the house level and then we use that rainwater for our garden. That pipe is close to 40 years old and it seems like it has cracked or developed some other kind of leak because the wall is getting wet every time it rains.
Is there a way to seal the leaks in the PVC pipe from the inside, i.e. some kind of liquid which could be poured and allowed it to fill the pipe (closing the pipe at the bottom end) and then after the "magic" happens to be drained from the pipe leaving all the cracks fixed? Or any other solution other than tearing down the wall.

Sorry! No magic fix here! What I would do, if I didn't want t0 replace the pipe, is seal it off at the bottom, fill it wirh water and mark the cracks it's leaking from. Drain the water and let the pipe completely dry out. Now purchase a small can of clear primer and a small can of PVC cement. Making sure the cracks are dry prime and then pour PVC cement in the cracks. Let it set up for a hour or so and do it it again for insurance. Good luck and thank you for rating my answer. Tom

Thank you for the suggestion but you're forgetting that the pipe is IN the wall. In order to see the leaks I have to dig through the wall and since I don't know where they exactly are I would have to tear the entire wall down. Thanks anyway.

I didn't forget. You didn't think you could repair the leaks without first locating them did you? Open up the wall where you see moisture and follow the directions I gave you. Good luck, Tom

Or you can plug the pipe on the roof-level and by-pass it with new pipe mounted on the exterior wall. Otherwise, you will have to cut open your walls.

Yep no magic fix here. You have been given two fixes which both work. The other fix would be to abandon the system and cap it, drain your gutters down a down spout like 99% of the other homes