Your current plan is no good -- first off, 400.8 forbids the use of cords as a replacement for permanent wiring (stuffing a cord down a conduit certainly counts). Second, 400.9 prohibits the splicing of cord during installation. Third, wire splices need to be in a junction box so that they can be serviced in the future.
A better plan would be to bring the conduit out to the receptacle box where you plan to tap power, and then stuffing NM through the conduit (yes, this is OK). At the box end, you'd simply tie it into the rest of the wiring as you would ordinarily (using pigtails and wire nuts if they aren't already present there). At the monitor end, you'd attach a field-fittable IEC C13 connector directly to the NM cable and plug it into the monitor (you may need a right angle connector here -- make sure it accepts 14AWG as not all do).