depends what you mean access. They can contact it (assuming its a public IP), but nothing more unless you have no NAT or firewall (assuming there's no allowed ports on the firewall)
This thread has now gave me the guts to ask a retarded question... You know those Sci-fi movies about hackers accessing restricted access PC systems, stealing data & such using "movie depicted" password hacking applets or warez. Are those real? I mean are there people really doing that?
Hacking is a bit more harder than just going "la i on ur computr steeling ur stufz" but it can be done to a certain extant. It's also possible to access someone else's computer with Remote Desktops, which also requires IPs, but is not hacking (Remote Desktops are terribly limited)
Well, my older brother used to hack other people's computers (he did get caught), so yes, people do, do it.
It depends. Security vulnerabilities always exist, it's just a matter of if the solution you have protects against them. In your case, it's hard to access someone's PC unless there was, say, a vulnerability discovered for mIRC that'd allow a person to execute code on your system. Using this, they could drop a trojan onto your system and thus take control of your PC. Using things like Windows Firewall make it harder but not impossible. The lack of a router acting as a hardware firewall or stopping things through NAT traversal make things easier for the attacker. As the old saying goes, 'never say never.'--it's just an issue with time, effort, and if it's worth it... and it often isn't.
Remote desktops aren't limited, you can do anything that you could do at the machine (while the OS is running anyway), but for a hacker to attack a PC with it, the service has to be running on the target PC (Windows remote desktop is not enabled by default), there needs to be the correct port opened in the firewall/forwarded on the router, and the hacker needs to know the IP and the username and password.