Hi there Roger and welcome
On problem Laptop
Please click on Start->All Programs->Accessories, then right-click on Command Prompt and click on Run as administrator. Then type each of the command lines below, one line at a time, and press the Enter key each time:
netsh winsock reset
netsh int ip reset netshlog.txt
Then restart the Laptop and check if it now has internet.
Let me know the results please