Sorry to hear that you weren't able to place towers! A few potential reasons off the top of my head for your issue:
1) There is collision detection active on placing towers on the map. If you attempt to place a tower too close to another structure (not including the enemy projectiles), then you will not be able to create a tower there. We likely should have added some visual indication of whether placement was allowed, or a sound if you couldn't place at that time.
2) If you weren't aware of the mechanic that tower health decays over time, then you might not have noticed that some towers were being destroyed when you placed new ones.
Does it seem like either of these could have been your issue? Otherwise, apologies, and thank you for trying to play!