Same thing happened to me once, complete failure (due to an insect in the system) on take off from Dinard to Bournemouth. It was an early morning flight, quite hazy and hot. Just got airborne, checked the ASI on the climb out and was surprised to see it reading 100mph. Pulled the nose back to get the correct climb speed and felt a slight shudder go through the aircraft, as I was thinking to myself "that felt like a pre-cursor to a stall" the stall warning light flickered on and off. I put the nose down slightly and checked the ASI and to my great surprise it was indicating 130mph and rising !
Realising something was far from right I put the nose down and flew over Dinard at 500 feet while I tried to get my head around what was happening
Anyway, analysing things afterwards three thing where very clear.
1) The loss of the ASI itself is not the end of the world. The real threat to safety is the time it takes you realise what is going on and then to take the correct action. I suspect this can be the case with other in flight problems
2) I consider myself lucky
3) If this had have happened (during the climb after take off) in IMC I would not be writing this now
Regards
FBW