Engine will not start and run?

The oil pressure switch can cause a non starting situation. Distributor or distributorless, turning the crankshaft to get the pistons to TDC uses the same technique. When you turn the key to the on position without cranking the engine over can you hear the fuel pump run in the tank for 5 seconds?

https://www.2carpros.com/articles/car-cranks-but-wont-start

Please run down this guide and report back.

Taking the cam sensor out should not cause it to jump time but if the wire connector is not secure, that could cause problems.

Symptoms indicates a possible ignition switch problem but I am not too sure if I understand your description correctly.

If you are able to crank without engine starting, you should be checking through the link.
What makes you think the cam sensor is faulty in the first place?

The sensor is only plugged in so you should ensure it is correctly seated and secured. Ensure the wire connectors are plugged in correctly as well.

You pulled this out and yes, it affects the timing if it is not correctly installed. Here are the procedures to get it back into position.

Installation

NOTE:
Fuel system synchronization is controlled by position of oil pump drive shaft assembly.

1. Clean oil pump drive mounting hole area of engine block. Install NEW oil pump drive shaft assembly-to-engine block gasket. Temporarily install a pin punch or drift through access hole on side of oil pump drive housing. Align hole on pulse ring with hole in
housing. See Fig. 57.

2. If engine crankshaft or camshaft was not rotated, go to next step. If engine crankshaft or camshaft was rotated, CMP sensor relationship must be adjusted, go to step 4.

3. Install oil pump drive shaft assembly into engine while aligning oil pump slot. Rotate oil pump drive shaft assembly to its original position. Install hold-down bolt finger tight. Go to step 5.

CAUTION:
DO NOT rotate engine against normal rotation to align
timing marks.

4. Remove ignition coil rail assembly. Remove cylinder No. 1 spark plug. Rotate engine (in direction of normal rotation) until pressure is felt in cylinder No. 1. Slowly continue to rotate engine until timing mark aligns with Top Dead Center (TDC) (zero degrees) on
timing scale. Install oil pump drive shaft. If oil pump drive does not drop down flush with engine block, oil pump slot is not aligned properly. Remove oil pump drive shaft and rotate so oil pump slot aligns with shaft on bottom of oil pump drive shaft. Install oil
pump drive shaft and rotate oil pump drive shaft assembly to its original position. Install hold-down bolt finger tight. Go to next step.

5. Remove pin punch or drift from oil pump drive shaft assembly. Install CMP sensor onto oil pump drive shaft assembly. CMP sensor connector should be facing rear of engine (zero degrees). Connect CMP sensor connector. Install spark plug and ignition coil rail
assembly (if removed). Go to next step.

6. To verify correct rotational position of oil pump drive, DRBIII
 scan tool must be used. Connect DRBIII scan tool to Data Link Connector (DLC), located below driver's side of instrument panel, near steering column. Start engine. Ensure engine is at normal
operating temperature. With engine idling, select SET SYNC from scan tool menu. Observe scan tool display.

7. If scan tool displays IN RANGE and zero degrees, procedure is complete. If scan tool does not display IN RANGE and zero degrees, loosen hold-down clamp bolt and rotate oil pump drive shaft assembly until reading is as close to zero degrees as possible, and IN RANGE message is displayed. Tighten hold-down clamp bolt to specification. Turn engine off. Remove scan tool.

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I am not sure what noise that is so you would have to fill me in with as much information as possible. Have you rechecked the installation of the camsensor gears as getting the gear off by a mark can cause performance and running problems. Did you try manually adjusting the cam sensor timing? Since you don't have the scan tool to check the timing, you might have to manually adjust it manually. Turn engine off. Mark the initial position and loosen the holding bolt and turn the shaft clockwise slightly and retighten. Try starting and and note if there are any changes. You might have to repeat with a few adjustment to get the best result. You might need to go counter-clockwise instead of clockwise.

Since oil pressure is available, it is less of a worry.

If it is from top of engine, the components likely to cause noises would be the valve lifters. Is it more of a tapping type of noise?

Remove the oil filler cap and look into the valve cover and note if oil is getting to the top. You need to start engine and chack.

DO NOT use any additives. A little running should quieten down the noise.
Yes, the timing could be off and I had old you how to go about since you do not have the appropriate scan tool to check the timing.

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