Best way to go about it is to use a VPN. Check out Witopia VPN. Sure its going to cost something like $70/year and throttle your internet speeds a bit, but its the best way to circumvent any problems that have to do with a static IP address.
Firstly you will never lose files from an IP address change on a local machine.
Secondly, depending on what the hackers are doing, changing the IP address on your local machine may not be enough. You may have to change the IP address of your Router, or even get your ISP to change the IP address on their end. If you have a trojan or some other kind of virus on your machine then you'll need to clean it prior to doing this. If you visit websites that give you such things then you'll need to stop visiting them to protect yourself.
Without knowing what they're doing then a simple IP address change may not even stop them.
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.