Why isn't my iPod turing on or charging?

I have an old, broken iPod g3, but since I'm only barely a teenager I have no idea what to do. I also have no money to invest in repairing, as my parents do not want to get it repaired and almost threw it away. It started randomly turning off in blasts of random colors, and one day it did that and wouldn't turn on. When I try to plug it in to my computer, it shows up but is not able to be recognized or even accessed. When I try plugging it into

My fake iHome it makes a quiet distorted sound through the iHome. I honestly have no idea if I should just give up and throw it away or attempt to fix it.