@koh I was having a similar problem. I would fall down when trying to ascend without any weight. What helped me with a squat was flexing my core when ascending - it really helps to hold balance. I had tried leg presses (horizontal and vertical), but now that I can do squats (last time I did them with a 10 kg barbell), I would suggest doing squats even if you have to hold on to something (like a ladder) to get up, because leg presses are not the same and they didn't help me to get to doing a squat.
Also, try to do it at home barefoot - shoes can be really not squat-compatible and maybe that's the problem.
So, 1) try to do it barefoot and see whether the shoes are the problem
2) flex your core muscles and glutes when ascending
3) try to squat at home instead of sitting sometimes. You can get up however you can, but this should improve flexibility
4) continue doing squats at the gym, but if you cannot ascent, hold on to something until you don't have to anymore
5) if it hurts, maybe see a doctor
Hope it helps, but as you can probably see from the weight I'm using, I am not super experienced. Maybe someone with more exp will come by and answer your question better.