2003 Hyundai Just stopped on parkway!

I recently purchased a 2003 Hyundai Elantra that had 33,000 miles on it. I was driving down the Garden State Parkway when the power started to die on the car. The tow person felt that it was the timing belt that had gone and I had the car towed to Hyundai for service. Hyundai is stating that it is the water pump that is the problem. Woudl the water pump cause the car to just die? Wouldn't I have seen an anti freeze leak prior to the car simply stopping? The car now only has 41,000 miles on it but the dealer that I purchased it from does not do repairs.

Any suggestions/help? I am not sure what questions to even ask!

Thank you!!