No ohms or resistance is an internal open. Unless designed that way, the sensor is toast. Reading ohms quickly determines if a sensor is bad. For sensors that move/click with 12V, you can test those with jumper wires. I like to use a Power Probe IV to test solenoids, light bulbs, fans, emissions valves, and other 12V components.

This has become a tedious problem for me. I just found out that the ground wire on the harness plug has no continuity and the measured resistance by multimeter is very high, around 4 mega ohms! That's probably why the sensor's acting up.
I tested the exhaust CPS, and its ground wire does have continuity and shows almost zero for resistance. The visual inspection of this wire & harness reveals nothing unusual; and the wire bundle from the harness to the carrier control unit looks well sealed and untouched. I punched a needle hole immediately behind the plug on the ground wire and found continuity across the plug. But the wire seems to be shorted somewhere beyond the plug. Please excuse my ignorance if I'm not using the correct terminology. I'm a novice diyer. Any guidance will be much appreciated.

I think you are going down another rabbit hole with the cam sensors but while you're there check the red/white wire for 12 volts in reference to a body or engine ground NOT a wire in the harness that you think is ground.

After that if you have triple checked your work then start over and diagnose as a no-start checking for spark and fuel pressure.

BTW you can very easily ruin an injector by putting 12v to it. AND very easily ruin the DME by trying to power the injectors while they are connected!

I have 12v on thé middle prong and 4.5 V on one of thé outer prong. So the third prong is the ground. That's the one I'm talking about. I checked the CPS on the exhaust side which turned out to be fine. So only that ground wire on the intake side is the problem now.

There is no actual ground only 12v power from a fuse, both other wires go to the DME.

When you had the battery disconnected it sounds like you didn't disconnect the battery at the battery terminal but where the cable attaches to a stud?? Are you sure there wasn't another ground connection still in play??

First time I disconnected both battery terminals. But the second time I only disconnected the negative terminal. And no, there is no other ground terminal that I messed with.
And btw, on the exhaust CPS the third prong prove to be correctly connected to the ground via DME of course. If you connect that prong to one of the terminals of multimeter and connect the other terminal of the multimeter to the car body ground you get continuity. That's what I did for the exhaust side and it worked. But doesn't work for the intake side.

The intake CPS side has a harness that goes under the filter and power steering areas, right? I have not changed mine but I've seen sensor pictures. If ground is going across the plug but not when plugged in, the plug is suspect. Can it be opened for inspection? I follow Pine Hollow Auto Diagnostics on YouTube. His videos have taught me a lot. He has so many videos of vehicles diagnosed with bad connections. Corrosion, salted roads, and water cause all kinds of electrical problems.

Please see the attached video explaining the situation. Sorry for my slow talk, it's first thing in the morning for me. The plug is good, the ground wire is not.

https://youtu.be/TenrMP-DCGk

Any luck? Is the ground DME ground? Or is it body ground? I have not looked at a diagram. If it's body ground, make a bypass and crank to see if it starts. If it's a DME ground, that's no easy task to apply ground.