The ability to provide an IP address to law enforcement might be able to help in tracking down the computer, but no guarantees. At the very least, it will likely involve a lot of red tape. Many companies and ISPs will only provide subscriber information when instructed to by a court etc. This can become tricky if there are state/country boarders involved. IP addresses are frequently allocated dynamically and being able to track who was using a specific IP at a specific time depends on how good/reliable (and possibly how far back) log records are maintained. In some countries, organisations don't retain log records for long to prevent the costs and complications that can arise from court discovery orders etc.
Of course, this all assumes the people who are using the computer are not smart enough to hide their real IP or even that those who used the computer are the same people who stole it. It may already have been passed/sold on.
The other issue you are likely to run into is lack of resources within the law enforcement area. Computers, especially laptops, are items regularly stolen. Police usually don't have the resources to track down each and every case. In most cases, when you ahve been burgled, the most you can hope for is that everything is covered by insurance.
Something which I think is very important to mention is that apart from your photos, have you given thought to what other important information someone could get from you computer? Did you ever use that computer for internet banking, on-line shopping with a credit card etc? If so, it is very likely that there is lots of very valuable information on that computer relating to your finances. I would be changing all my passwords, notifying my credit card company to cancel/re-issue my credit cards and watching all my statements very carefully.
A typical sequenc of events with a stolen computer is
- Thief steals computer
- Thief sells computer to someone who is more computer literate/interested than they are.
- New owner, who is likely a bit more rehearsed and knowledgable about computers and computer crime, connects the computer to the internet in a secure way (i.e. spoofs IP addresses etc). Uses the computer and the data on it (browser history, saved passwords, data caches etc) to gather information about the victim, either to assist in an ID theft process, make purchases using stolen credit card information or possibly try to access internet banking services etc.
- After data mining the stolen computer, they wipe it clean and either sell it on or dispose of it.
Sadly, I suspect your photos are gone for good. Unfortunately, this may not be the end of your problems. Think about what other personal/sensitive data may be on that computer and what it may be used for. If you think there is even the slightest possibility that your bank accounts, credit cards etc may be compromised, contact the necessary authorities and get accounts/cards changed. Play it safe - a lot of work, but a lot less hassle than trying to get things fixed after the damage is done.