1*Samsung 840 EVO 120GB SSD;
1*OCZ Vertex 2 60GB SSD;
2*Samsung F3 SpinPoint 1TB in RAID0;
1*Samsung F1 SpinPoint 1TB;
2*Western Digital 1TB External USB 3.0
1*Western Digital 500GB External USB 3.0
1*Seagate 500GB External USB 2.0
PSU
Thermaltake ToughPower QFan 750W
Case
Thermaltake Element S VK60001W2Z
Cooling
Corsair H60 Water Cooling, 2*230mm and 2*80mm case fans
There is really very little you can do with an IP address. You cannot obtain the individuals name, address, or other personal details. And that IP address may not be that of an individual at all but of some public Internet access point.
It greatly depends on the security configuration on the target computer. I will suppose for all this that we're speaking about public IP and attacks over internet (not LAN).
At the very minimum, you can ping it if the router it's not configured to reject those. This open a clear route for a DoS attack (or it's distributed twin, the DDoS), which can make the connection of the target quite slow or totally unavailable if your bandwidth is greater. That's a quite common way for hackers to take websites down.
Then, you can attempt a port scan to discover open ports and listening services on that host. If there's something "alive" there, there is a chance to find something with a security vulnerability, a weak password or just to flood with dummy requests.
All that of course relies heavility onwhat do your find and how many security vulnerabilities are out there. A properly secured computer will most likely not have much to do, and for sure it's not a straigforward way to break into someone else computer, much less to completely take control of it.
My Computer
Computer type
Laptop
Computer Manufacturer/Model Number
Toshiba Sattelite A665-S6092
OS
Windows 7 Ultimate x64
CPU
Intel Core i7-740QM
Memory
8 GB DDR3
Graphics Card(s)
NVIDIA GeForce 330GT
Screen Resolution
1366x768
Hard Drives
Samsung 840 SSD 500GB
1TB USB3 external HD
Cooling
Coolermaster Notepal U3 notebook cooling pad
Internet Speed
3mbps ASDL
Antivirus
ClamWin 0.98.7
Browser
Opera 12.17 x86 (main), Firefox 38 (sec), IE11 (last resort)