The computer is old and has some problems should I bother fixing?

My Mum bought the computer a few years ago, and then it broke a few years later. She bought a new one since, and this ones just been sitting on the desk not being used. I was hoping to be able to use this one. It is currently running OSX Leopard 10.5.8. It has 2GB of RAM in two 1GB slots. It is the 20-inch model with a 2.66 GHz Core 2 Processor. I'm not two sure what the Hard Drive Capacity is though.

It has a few problems, it shuts down randomly, the display turns off and on again occationally and programs load very slowly. It is also full of dust because it hasn't been used for years.

I've cleaned some of the dust out. I was planning to replace the RAM the two 2GB sticks so I would run fast. I was also hoping to restore and erase all the data from the computer in case there are any viruses and also to get rid of my Mum's old documents. And also upgrade the OS to Yosemite.

I don't know much about computers and I'm 16 and don't have much money to spend repairing it. I just want to use it to watch youtube videos, do school work so I don't need it to run super fast.

It's about 14 or 15 years old, so I was wondering if it's worth fixing at this point?