Why does my Vauxhall Omega engine light come on, and some other problems?

It is a year 2000 Omega 2.0 16 v. The car has 110000 miles with full service history. When the car is started from cold there is a whirring noise for about 1 minute from the engine which then stops completely. I have been informed that this may be the air conditioning trying to start up although there is no gas in it. The engine management light comes on sometimes and when on the car can lose power for no reason. The exhaust sounds hoarse but im informed has no holes. One garage said my cat was blown, another said it wasn't and they cleaned the lambda sensor which hasn't helped. Also until at operating temperature the engine, or front of exhaust seems to make a tappety noise. Not very mechanically minded so all help and advice appreciated. Thanks