Depends...
Obviously if someone gives true personal details to a site, then they can often find them.
The system can track the address of where the data came from. However that doesn't get you back to a person.
First problem is that the address isn't your machine, it's the one given to the router/firewall at your home. That is changed every so often, so if the ISP hasn't kept the record then the trail is lost.
However, several people may be sharing the connection, and the MN site will get the same address for all of them. It may log which browser you use, but that's probably not enough.
Many routers are wireless, and the default for most has been open access. Which means your neighbours can use your link. The way many wireless card in PCs work, they will attach to the strongest signal, which means they may do this quite accidentally.
Many "protect" their networks with WEP. This is so insecure that there are races for who can crack it the quickest.
Thus all the police can prove is that the post came from somewhere near your home, or more pedantically that it went near your home en route, since I have stuff on my PC that lets me drive other PCs remotely.
My s/w is for benign use, (honest guv), but there is an industry of people producing s/w that subverts your PC for dodgy activities. For instance, much of the spam in the world comes from computer zombies in thrall to such malware. So proving "you" sent something is quite hard.
They would need other stuff to really prove that you personally did it. At the moment they get convictions by lying and relying upon the technical ignorance of the judiciary.
There is no equivalent of fingerprinting.
Your PC does contain a unique MAC address, burned into a chip, many newer machines have 2, one for wireless and one for wired networking. This can be matched to a PC,
except of course my firewall has been configured to screw with that, and s/w on the PC can make sure it never even gets that far.
Also, there are many public PCs out there in libraries etc.