Installing a game (or other software) on a work computer (issues)

[TwoRoomsOneDoor]

BACKGROUND: Last week, I started teaching in a private middle school; it is the first 9-5 job I've had in my entire life. While I find it very rewarding and actually look forward to going to work each day, there is a TON of down time (at least 3 hours) in which I have nothing to do, even after planning lessons and checking work. Although I'm sure this will change, at the time being it is becoming pretty much unbearable and I am looking for a way to change it.

SITUATION: In each of our rooms (the room is basically mine; the prinicpal teaches 2 classes in there a day but she is usually in and out becuase she is so busy) we have nice new PCs. I have no idea what the specs are but I'm sure they are pretty decent. These computers are basically all free space and are only used by the school to access the internet and education resources. So far I have entertained myself by surfing the web, but 1) this gets boring for me quickly and 2) sites like this are blacklisted, preventing me from accessing a lot of interesting things. The school is very protective of the network but I have not seen any rules anywhere which prohibit teachers from installing non-malicious software onto a computer. At the end of the day, the computer belongs to the school, but I am basically leasing it for a year. We are a small school and we only have one tech guy, who takes his job pretty seriously.
Now, as a new teacher, I certainly would not describe myself as "indispensible", but I would say that I'm about 99% sure that they would not fire me over this (or anything short of molesting a student to be honest, considering the difficulty of finding a replacement and my good reputation). I am also confident that it would not affect my being offered a contract renewal next year, although I could be wrong about that. My questions are:

1. Is installing a game or other software on a school computer a really bad idea? Will I get in more trouble than I am thinking if I get caught?

2. Is it likely that someone will check through my computer at some point to see if I've installed anything?

3. Any other recommendations to alleviate boredom? I currently spend a lot of time on fantasy sports.

I'm hoping that people with real work experience can give me some insight here. I know it's a little stupid but 1) I would really like to not be bored and 2) I have been using a Mac Laptop for the past 3 years and there are a LOT of PC games that I have missed and would like to try. I will never play during class, just during empty hours when I have nothing better to do.