I see an education is in order. Very little in your question makes any sense.
An IP address is generally dynamically assigned to you by your ISP. For DSL/Cable, you will likely have the same IP address for long periods of time but it can and does change. Since the IP address is owned by your ISP, there is no personal information involved with it. The only thing an IP address does is tell other computers on the internet how to find your computer. It is similar to your snail mail address as the postal service needs the address to deliver mail. The difference is the IP address doesn't reference a physical location other than perhaps the local office where the ISP's server is located. Your IP address is given out every time you access anything on the internet so that the servers can send information back to you.
So, just having your IP address does not allow anyone to have any personal information. If the police are agreeing that having an IP address means someone can steal your identity, then they don't know any more than you do. If there is a real problem, you may need to go a bit higher to the state police or maybe higher until you find someone who can actually investigate computer crime. It is possible they blew you off because you don't appear to know what you are talking about.
On to the real problem. The most likely scenario is you have a piece of malware on your computer or perhaps that you freely gave the information to a fake website. In the first case, it might be a Trojan horse, RAT or even a root kit. Key loggers, remote control, remote access, screen captures, and even live screen feeds are possible. You need to do a full system scan with your anti-virus program and make sure that both the program and it's virus definitions are current.
If you got tricked by a fake website, you may not know when it happened. The attack can be that sneaky though at the time, you may have noticed something was slightly off.
If you do find malware, you may need to start identity theft recovery. It depends on what information they actually have. Once you are sure your system is clean, I would suggest that you systematically go through all your accounts and change all the passwords. This may be all that is needed unless they did further damage. Only time will tell and serious identity theft can take up to a year or more to recover from if the various articles I've read about it are true.
Much of this is guess work since I would need a lot more information to make any other suggestions. It may be that you only lost a few accounts and that isn't really identity theft.
Shadow Wolf