Mountain bike gear problems / shifting?

I have a Giant 24speed Mt Bike and the shifter on the left hand side won't work. It clicks but the derailer/chain doesn't do anything. First of all is there a name for those gears? Is it the high or low or just the left hand side gears? Well to explain there are 3 rings on one end and 8 rings on the rear wheel, it's the 3 rings that won't shift...it's stuck on 1.

I was able to take a look and I see that there seems to be a lot of slack in the cable. I just used my bike the other day and it was working fine. Then I go out today and it wouldn't shift which seems odd.

Its dark out now I can't see much and I'm really hoping it's just a matter of me tightening that cable.

Do you need special screwdrivers to fix the derailers or tighten those cables?

-How about some opinions on Mt Bikes...My Giant is a hand me down from my brother. It's worked great over the years and I would consider my self an extreme rider ie: I ride down the steepest and bumpiest trails hitting huge rocks and roots and the bike seems to be in great shape with little maintenance. I know people who hit these bumps and their chains fall off. If I wanted to get a new bike what would you recommend for an extreme rider for under $1,000? Thanks all for your advice and happy trails.
Oh also, what sets say a $1,000 mt bike aside from a $300 one? Is it that you're just paying extra to have something lighter?
 
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