Alright so we can rule out a cable problem.
I know I have nightmares trying to connect my old Xbox to the PC, somedays it works and then other times it doesn't. Security updates tend to cause hassles with these connections at times.
Right could you explain how you are connecting your 360 to the PC, is it connecting to a network card in your machine which is in turn sharing your internet connection?
Or are you connecting it to a router?
One thing you need to be careful about is when you change the IP on the PC, I assume you have a USB connection coming into the laptop for the internet connection, you need to make sure you are changing the IP for the network card that connects to your 360. You don't wanna play with the other setting.
Should normally be "Local Connection 2"
If it worked previously then we shouldn't really need to mess around with IP's and the likes so lets try the following.
Change both the PC and the 360's IP to automatic detect. Then power down both systems.
Now turn the PC on and get into windows, once there turn the 360 on and see if you can connect.
If it doesn't work then try it the other way round, so turn the 360 on first and then the PC.