You wrote in detail the Watts, Volts and more. Let's skip to the bottom line and recall a little history.
Given the same polarity, Volts, Watts and amperes all looks ready to plug it in. HOWEVER due to (google this!) laptop battery fires there is some smarts in today's laptops that talk with the power brick (it's not a cord) and if it's not supported you should see nothing happen or maybe a message such as "Plugged in, not charging."
I just got a new Dell Inspiron 15R laptop. The power cord that came with the laptop is marked Dell 90W AC Adaptor, Input AC 100 - 240V - 1.5A, Output DC 19.5V - 4.62A. It has a grounded 3 prong wall plug.
I have another power cord from an old Dell laptop with the exact same ratings (marked 90W AC Adapter with identical input and output specs). The old cord has a 2 prong wall plug with both prongs the same size - so I assume the wall plug on the old cord is not polarized.
Can I use the old cord on the new computer? I don't know anything about electrical issues so I would appreciate any advice. Thanks