Why is my car hard to start when cold but otherwise runs fine?

Its a 1998 model SB Barina, (Corsa B) with an opel engine. Its fuel injected. It starts fine when warm, and still idles and runs smooth once it starts, and, is not underpowered at all (other than the obvious standard underpowered condition of a 1.4litre engine, that is! DOH!!) When its cold, it takes a long time... show more Its a 1998 model SB Barina, (Corsa B) with an opel engine. Its fuel injected. It starts fine when warm, and still idles and runs smooth once it starts, and, is not underpowered at all (other than the obvious standard underpowered condition of a 1.4litre engine, that is! DOH!!) When its cold, it takes a long time before it starts, it just keeps turning over for ages and then when it finally fires it coughs and splutters and sounds like it is running on 2 or 3 cylinders for 10 or 15 secs before running fine from then on. I did a check on the codes and all I gotr was a faulty oxygen sensor which I have since replaced, but it made no difference to the starting. I checked the code again and it says the oxygen sensor is working now. I'm thinking maybe leaking injector/s dripping fuel into the manifold making it too rich and not firing till the excess fuel is out of the cylinder. I am not sure how to check this, and I was hoping some mechanics out there might give me some other things to check. It is embarrassing in the morning when all the neighbours hear me taking ages to get it going. Thanks in advance for any advice.
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