Huge post ftw.
Depending on the type of router you have, you might be able to increase the DHCP range to fix it (assuming that's the problem anyway).
Find a computer that's able to connect to the wireless, and open up a browser and go to the IP of the router (typically it'll be 192.168.1.254 or 192.168.1.1, but it depends how it was all set up - if neither of those work, use "ipconfig /all", find the main wireless connection, and there should be something like "Default Gateway" which I believe is the router IP).
You'll need the login info for your router. Some routers will have the fabulously secure default of "admin" being the username and no password, others will have randomly generated passwords, so hopefully you or your dad know the login.
From there you'll want to find something along the lines of DHCP settings or DHCP range. It'll be something like 192.168.1.100 ~ 150 (again, depends on how it was set up), so just increase the range between those by 20 or so and see if it helps.
If you can't log in to your router, or you can't find the DHCP settings page (some routers don't let you adjust the range), use "ipconfig /all" on a few computers that are connected to the wireless to check their IPs and get an idea of where the range starts. (So for example if they end in 51, 52, 54, 57, etc. your range probably starts at 50 or so). Also, write down the info for (these 3 things should theoretically be the same on all the computers):
-Default Gateway
-Subnet Mask
-DNS Servers (there's usually two of them listed, if there's more than that just write down the top two)
Then go back to your laptop and (I'm assuming Windows 7 here), go to Control Panel -> Network and Internet -> Network and Sharing Center -> Change Adapter Settings.
Find the wireless adapter (which should just be named "Wireless Network Connection"), right click it, and click "Properties". In the list of random gibberish in the Networking tab, find "Internet Protocol Version 4 (TCP/IPv4)", click it, and click the "Properties" button.
Click the bubble for "Use the following IP address", and put in an IP that's just slightly below the range you found above (so in my example, something like 192.168.1.40 should work). Then use the stuff you wrote down earlier to fill the rest of the lines out, and click OK. You might have to disable and re-enable the adapter to make the changes take effect (I don't think you have to, but Windows can be picky sometimes). From there try to connect to the Internet and see if it lets you connect.
Hopefully that'll fix it for you, but if it doesn't you'll probably want to go back and click the other bubbles for getting your IP and DNS settings automatically, since typically you don't want a static IP unless you need to have it set to connect (or if you're doing crazy stuff like hosting).
If the DHCP range / static IP don't help then it's most likely an issue with the laptop as opposed to the router's DHCP, so you might want to have it looked at.
PS - I have a tendency to forget to check back on topics I've posted in, so if you need clarification or anything and I don't reply here you can feel free to add me on Skype (my Skype user is encon21) and I'll try to help you out. :3
