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There is not typically a mapping between mac addresses to IP addresses. But if you flip the question around, can I get a mac address based on a specific IP address then yes. If the two devices are on the same subnet, just ping the host and then look at the output of the command arp -a You could combine a ping sweep with outputs of arp -a >>mactable.txt to get an association. Understand this is the bruit force way to go about it with only having windows. You could also run an nmap (zenmap) scan of a subnet range, mac address is one of the reported values of the scan.
[edit] Rereading the question I totally missed the topic of the question. The above is of no use. What serial numbers are you referring to? Is it the serial of the motherboard/chassis or are you asking for software licensing based on the mac address? Spiceworks is a great tool. You could probably write a powershell script to grab the computer name and serial number and then use the computer name to grab the mac address. I'm not a powershell person but I found these code snippets that will get you started.
Submerge Serial Number Mac Download Windows 10
And this to get the mac address