Laguna heater/ac blower fan faulty

I have a 2002 model renault laguna, 1.8 Automatic. At first I have drops of water sometimes a bit more coming from below the glove box and drips in the carpet (on the passenger side).

Recently, the fan doesnt switch on. At times the fan just starts for 2 to 4 seconds and then stops. Without a hot air fan, there is mist formation inside the front windshield and all windows making it difficult to drive with poor visibility. Not to mention it is very cold inside without the hot air fan.

So the problem is this, The fan doesnt switch on. Even if i keep the blower setting on 4, it sometimes comes briefly on, for a few seconds, and then goes off by itself. I suspect some electrical fault. Can anyone guide me here?

Sam