ASCOM should be able to connect but I would try some other astronomy software too just in case it's ASCOM configuration issues. I'm not familiar with the nexstar to know how easy it is to configure with ASCOM. ASCOM typically requires some patients and learning.
Many use ASCOM, some don't. Most cost money.
TheSky,
StarryNight,
Cartes Du Ciel (uses ASCOM). I'm not familiar with any other than TheSky. I thought Celestron scope's came with one?