I doubt any hackers are terrorizing you.
It is likely a script kiddie, malware, virus, trojan etc. that is causing your problems.
Changing your IP will only help if someone decided to attack your network, using something like a syn flood, which I doubt they would waste on a privately owned (probably home) network. Not much reason for that, unless you pissed someone with a botnet off?
As previously mentioned your IP will likely cycle if its dynamically provided by your ISP.. You can sometimes force a re-assingnment by powering off your modem and plugging it back in after a bit, or requesting a change from your ISP.
If you gave more details on your issues people could assist you more.