There are many ways to attack someones computer if you know their ip. However, I wouldn't do it unless you really hold a grudge. If someone attacks my computer, or even hints, I generally let their ISP know about it and they'll shut them down (usually).
About rebooting someone's computer, you can't do it remotely only by knowing their ip, unless you know of, and have access to, a trojan type program on their computer, or know of a security hole in their OS or some service they're running that would allow you sufficient access to reboot their computer.
With the Halflife deal, as an initial guess, I'd say they're doing some form of a DOS attack to crash the other guy's computer, a ping flood is the easiest, though I wouldn't be suprised if there's some "feature" in Halflife that would allow you to achieve the same result. Make sure he knows that what he's doing is illegal, and if he hit the wrong person, he'd get blasted for it.
Next time you direct connect with him, do a netstat at your command prompt. No need for the -A. You're looking for an ESTABLISHED connection, his ip will be under the foreign address column, it's format is IP:PORT. His port makes no difference, there are literally thousands on everyone's computer, and it'll probably be different every time, don't remember for sure it's been awhile since I've looked at an AOL direct connect. Netstat is going to show all your internet connections, all the ones with port 5190 will be connections to the AOL IM server, and aren't what you want. If you can't figure out which one is his, post the output here and maybe I can figure it out.