I don't believe a hard start kit will provide any benefit if the compressor does not even move at all. It does increase the time during which a higher current into the start winding is available, and so the compressor would speed up faster or, if the inrush current period was too short, it will allow the compressor to reach its normal speed. But if the compressor has completely seized, a hard start kit won't do much.
There's a lot more information that needs to enter into this equation - type of compressor, type of its motor, type of hard-start kit etc. But in general, if you're looking to install one just to see the thing move at all, the compressor is probably [almost] shut anyway.
What happens if you let the AC sit longer between the cycles (so the system can equalize better and the compressor does not have to fight too high a pressure at the start)? Turn it off, let it sit for half an hour, then turn back on, see if it can start then. If it does start, a certified tech will need to look at the refrigerant lines.