These kinds of problems are very difficult to diagnose without being on site. Rather than guessing at a single fix, let me give you a process to follow. Think of electricity as a closed water system, with hot water coming in and cold water draining out. What we are looking for is a leak in the system. I'd start at the breaker. Check the load screw to the ground/neutral buss. 120vac ok? yes, then we move further down the line to the next possible junction point. At each subsequent point, check your hot side to neutral and to ground until you find the point where there is no longer a proper 120vac measurement. When you find this point, if you have 120 hot to ground, but not to the neutral, you have an open neutral. Turn OFF the power and check the neutral to ground with an ohm meter. It should be very close to 0 ohms. If you see no voltage to either neutral or ground, and the neutral to ground is 0 ohms, then you have an open hot. Check the input side of the GFIC and the load side in a similar method. If you try to follow a very straight logic, testing the three possibilites at each point,(open ground/open neutral/open hot) hopefully you will find the culprit. Good Luck
You're going to want to use a junction box to switch between nonmetallic sheathed cable, and individual wires.
Conduit body must be marked with volume
The first problem you'll run into while making splices in the conduit body (which isn't likely a problem, since most fittings are labeled), is that you'll have to make sure the conduit body is "durably and legibly marked by the manufacturer with their volume".
National Electrical Code 2014
Chapter 3 Wiring Methods and Materials
Article 314 Outlet, Device, Pull, and Junction Boxes; Conduit Bodies; Fittings; and Handhole Enclosures
314.16 Number of Conductors in Outlet, Device, and Junction Boxes, and Conduit Bodies.
(C) Conduit Bodies.
(2) With Splices, Taps, or Devices. Only those conduit bodies that are durably and legibly marked by the manufacturer with their volume shall be permitted to contain splices, taps, or devices. The maximum number of conductors shall be calculated in accordance with 314.16(B). Conduit bodies shall be supported in a rigid and secure manner.
Cable must be secured to conduit body
The next problem, is that the cable must be secured to the conduit body.
314.17 Conductors Entering Boxes, Conduit Bodies, or Fittings. Conductors entering boxes, conduit bodies, or fittings shall be protected from abrasion and shall comply with 314.17(A) through (D).
B) Metal Boxes and Conduit Bodies. Where metal boxes or conduit bodies are installed with messenger-supported wiring, open wiring on insulators, or concealed knob-andtube wiring, conductors shall enter through insulating bushings or, in dry locations, through flexible tubing extending from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamps. Except as provided in 300.15(C), the wiring shall be firmly secured to the box or conduit body. Where raceway or cable is installed with metal boxes or conduit bodies, the raceway or cable shall be secured to such boxes and conduit bodies.
(C) Nonmetallic Boxes and Conduit Bodies. Nonmetallic boxes and conduit bodies shall be suitable for the lowest temperature-rated conductor entering the box. Where nonmetallic boxes and conduit bodies are used with messengersupported wiring, open wiring on insulators, or concealed knob-and-tube wiring, the conductors shall enter the box through individual holes. Where flexible tubing is used to enclose the conductors, the tubing shall extend from the last insulating support to not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. Where nonmetallicsheathed cable or multiconductor Type UF cable is used, the sheath shall extend not less than 6 mm (1/4 in.) inside the box and beyond any cable clamp. In all instances, all permitted wiring methods shall be secured to the boxes.
Wet locations
If the conduit body is outside, the AHJ could consider it a wet location. In this case, you wouldn't be able to have NM cable in the conduit body since it's not allowed in wet locations.
tl;dr
In most cases, you'll install conduit off the back of a Type LB conduit body, through the wall, and connect it to a junction box inside the building. You'll make your splices in this box, not in the conduit body.
Best Answer
There should be no problem doing what you want, as long as all the conductors and overcurrent devices are sized properly. As per National Electrical Code, you'll size the equipment grounding conductor (EGC) based on the largest overcurrent device used. Which means the EGC will likely be sized based on the size of the breaker protecting the 240 volt circuit.