Errr quickly off the top of my head...
Ok, your dad's laptop connects ok, so the link from the router out is fine as you've mentioned. It's either your laptop itself, or the link between your laptop and the router.
Step 1 - see if laptop can reach the router, or even better, your dad's pc.
On your dad's pc navigate to Run --> CMD --> Type "ipconfig". Note down the ip address (will look like X.X.X.X where X = numbers).
From your pc, navigate to Run --> CMD --> and type "ping X.X.X.X" (where X.X.X.X = your dad's ip address).
If the reply's get through, and the connection is up it will say something like below...
Reply from X.X.X.X
Step 2- If that works, see if your PC can reach the internet...
If that works, can you try pinging again but this time "ping google.com"
If that works, then its probably something silly on your laptop, such as under File you have "work offline" ticked or similar!!
If not... well if not, can you please post the output of "IPCONFIG" from both your dad's and your PCs? as that will probably give us a good idea. Can you run through that and let us know how you get on?? and what happens? People on here can probably help you more after with that info :-)