Why won't car start with new camshaft?

Did you double check the timing marks on the crank & cam before installing the cover?

Both marks facing up. Use a straight edge; center of the crank though the mark on the gear to center of the cam through the dot. Then roll the engine by had & double check. Install the distributor, then start the engine before installing the timing cover. It's OK to run for a couple of seconds without coolant.

The back firing may be due to incorrect spark plug wiring

Firing order 1-8-4-3-6-5-7-2 Rotor turns clockwise. If OK then remove # 1 spark plug (driver's side front) Place your finger in the spark plug hole. Bump engine over with remote starter switch. When the compression pushes your finger align the timing marks to TDC. The Distributor cap will have the firing order stamped beside each spark plug lead. Drop the distributor in so it's pointing @ #7 wire. Push down on the base & crank the engine slightly until the distributor drops into the oil pump. Slide the retainer up against the base & snug, but don't tighten. Place your finger back over the hole & bump over again. Align the timing marks & locate the position of the rotor. Should be in-line with #1 spark plug lead.

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You more than likely have the distributor installed 180 degrees out. Pull the number one plug and stick your finger in the plug hole - tap the engine over with the starter until the compression blows against your finger - look at the timing mark, it should be close to the TDC mark. Align the marks on TDC and reinstall the distributor with the rotor pointing to number one plug terminal. Snug 'er down, set the timing with a light and enjoy your road test.

Sounds like the distributor is 180 degrees out

There is 2 top dead centers tdc on exhaust stoke and tdc on compression stroke.

Take the rocker cover of the bank that contain no1 cylinder and turn the motor over till both valves on no1 are closed on tdc (the rockers should move a bit) and see if the rotor arm is pointing to no1 post if not pull the distributor out and put it back so it points to no1 post.

It sounds like you may have misaligned the timing marks on the camshaft, or aligned them without the #1 cylinder being at tdc. Another possibility is not connecting the spark plug wires in the proper firing order. I know it means a lot of work, but I would check the timing sprockets first.

when i did a rebuild on my nissan i had a chilton manual and the diagram for the TDC timing was wrong. double check to make sure that the book showed the marked links on the chain and the marks on the timing gears in the right place.

your timing is out,you need to find where the cylinders have to be for ignition and then readjust.if you installed everything properly find where no.1 spark is take the timing chain off,take the spark plug out,with a torch make sure that cylinder is in correct pos.as in up for spark an put timing chain back on and see if that works ,if not see a mechanic.

Did you make sure that you had the spark plug wires installed in the correct sequence?