SL2 Indicator lights work for one turn then stop working, Hazard Lights don't work either

I have a 1999 Saturn SL2 with just over 100,000 miles on it. Recently I have been having issues with the indicators. I turn my left or right indicator on and it will sometimes work. However, usually, when I flip the indicator, nothing happens (no sound, no lights). I'd assume that all my indicators were burnt out, but they seem to work occasionally (usually only one or two turns at a time). I have also noticed that sometimes it works if rather than flipping the indicator all the way, I simply press it towards the left/right (up/down on the steering column) position, right before the trigger point. Oddly enough, I have discovered that by pressing the hazard light button on top of the steering column, this seems to allow me to get one or two signals out of the indicators (I can see the indicators light up and hear the blinking, when it is not working I flip the indicator and there is no light or blinking sound). The odd thing however is that the hazard light button itself appears to do nothing, as pressing it does not activate my hazards. What could be causing this?