[Solved]-LINQ approach to this code-LINQ,C#

This should do the trick:

return Properties.Any(x => !string.IsNullOrEmpty(x.SerialNumber));

I don't think you'll improve particularly on the performance of string.IsNullOrEmpty(), but one pitfall you should be avoiding is the last 2 calls on your query - specifically ToList() and Count().

What you are doing there is iterating through every element, converting it to a list (creating a list and adding items in the process, and then iterating through every element on the list to count how many there are - all to check if a single value is empty.

You can use the Any method to find if a single element matches certain criteria, like so:

return Properties.Any(x => !string.IsNullOrEmpty(x.SerialNumber));

Check out IEnumerable<T>.Any():

public bool HasSerialNumber()
{
    if(this.Properties != null)
        return Properties.Any(p => !string.IsNullOrEmpty(p.SerialNumer));
    return false;
}