If a guy you like is too shy to say Hi, and you've been chasing him for the longest time, should you just ignore him, or say hi first???

Say hi first with a smile (hopefully the shy dude will respond hi, if he doesn't then he's not shy but weird) . But don't take his contact yet.  Next time be real nice and engage him in a conversation around what he likes to do or is good.  This will make him feel comfortable around you.  Then you can take it from there.  But before wasting too much of your time you need to find out if there are signs a shy likes you.