Hi Luella,
It's possible you have a WiFi connection with your router, but there's a problem with IP addressing or the DNS information - do you know whether your wireless router is acting as a DHCP server? If so, both laptops should be configured to get their IP addresses and DNS info from the router. If the router is not acting as DHCP server, then both laptops need to be assigned unique "static" ip addresses in the range expected by the router. If using static-ip, copy the DNS information from working laptop to "old" one.
It's possible laptops are connecting to someone elses router - if I were you, I'd configure both my laptops to connect to "Access Point only" - NOT "Any Available network". On the old laptop, delete all existing Wireless Networks, and Add one new network with the details required by your router - i.e. SSID name, security settings. You should be able to copy these details from the working laptop (assuming it actually IS connecting to Your wireless router.)
It could well be some other detail that explains your connection difficulty!
"ipconfig" is a tool people sometimes use to check the health of their internet connection. On working laptop, open a command-prompt with admin priviledges, and type ipconfig [enter]. A list should appear with info about each Ethernet adapter including your wireless adapter. There should be a line that starts "IP Address..." and shows an address of 192.168... That's what you should see on the "old" laptop, but the IP address will be slightly different. If the old laptop shows an IP address of 0.0.0.0 or 169...., then the old laptop is having a problem obtainin its IP address. If IP address looks good, but still no connect, then double-check DNS settings...
Luck/Cheers!