Sounds like you've got water in the electrics big time. You need to try and dry things out. You could try spraying anything under the bonnet that is electrical, particularly connectors with WD40 this is designed to displace water, some people swear by it!
Depending on the size of the puddle and your speed you may have forced water into things that will need opening up to dry them out but I'd try the WD40 trick first -it's quick, cheap and easy!
Richard
December 2008