When you mentioned you cleaned it, did you take it completely apart?
It sounds like there is still remnants of the milk inside the laptop, which would cause parts to short (like the keyboard) and not let your laptop turn on, or make it freeze when it does.
If you feel comfortable taking apart the laptop, I suggest you look for a "how to" take apart your specific laptop model number.
Be warned - it can be a very long and tedious task, as well you have to be quite careful as laptop components are quite fragile.
You would need something like a lint-free cloth + 90% + Isopropyl alcohol to wipe off all the milk gunk off the motherboard (if it indeed got there) as well as underneath the keyboard. Anywhere it might have spilt.
When you use the alochol it does not need to be soaking wet - just damp.
You also might need some thermal paste for the CPU and GPU (if it has one) if the milk got on/near the heat sink of the CPU/GPU.
However - it is possible you may have permanently damaged the laptop if you turned it on while there was still milk inside.
Does your laptop cover accidental damage? You may want to contact HP if its still under warranty.