There're a few things to consider here:
- Do you have extensive knowlege of programming?
You need a good knowlege of programming and system internals to start using a debugger, if you don't then you should probably be looking at a memory trainer.
- Does the game have a CRC check?
Try modifying some of the bytes in one of the caves in the .text section of the exe and then every other section. See if you get banned for hacking or if you get a negative response.
- Do you know any ASM?
Debuggers such as Olly are useful really only if you know at least some assembly (or are smart enough to pick it up quickly by debugging)
- What are you trying to accomplish by using Olly?
Are you trying to patch the EXE permenantly or just trying to change some variables? If you're trying to change some variables then perhaps it's best that you write a loader instead
- Do you understand what packers are?
Most of the time you'll find that an EXE is packed, probably by ASProtect/ASPack or UPX. Do you know what that means and how it affects you? Many of these programs will implement anti-debugging measures, some of these (such as IsDebuggerPresent()) can be avoided by modification or (a better alternative) DLL injection or (even easier) a plugin to Olly. But you need to know how to find them and remove them - much like altering the Cyclic Redundancy Check to give positive feedback to the rest of the program.
I think what I'm getting at is that Olly isn't for people who "don't know nothin'" (unless you read that as a double negative) and that there are pre-packaged tools for people who just want to "train" the game.
Also, Olly breaks as soon as the windows loader reaches the OEP of the EXE, so you might want to press [F9] when you load an EXE up in it.
On further reading of your post it seems like your computer's slow and you should tune it a little (kill off your malware, prune your softwares.)
Hopefully that's food for thought for you or anyone else here.