When a double-hung window is stuck shut, resist the temptation to force it open with a pry bar, 2X4, or brute strength. You could crack the sash frame or shatter the glass. Instead, try a more thoughtful, safer approach.
Wearing leather work gloves and safety goggles, push a 4- or 6-inch-wide, stiff-blade putty knife into the joint between the sash and interior stop (the thin, vertical wood strip nailed to each side jamb). Also insert the putty knife into the joint at the top and bottom of the sash. As you force the knife blade into the joints, it will sever any spots that are adhered with dried paint.
To raise the sash, use the handles, if any, along the bottom sash rail or place one gloved hand on each upper corner of the sash frame and push up. Never lift a sash with one hand placed in the center of the upper rail — it might crack.
When all else fails, use a thin pry bar to carefully remove the interior stops to free the sash. They might not come out in one piece, but you can easily replace them with new stops.