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Keep it simple. Forget the computer controls, fuel pumps, injectors for the moment and start with the basics. All an engine needs is fuel, fire(spark) and compression to run. They also need to come together at the right time. You need to verify you are getting fuel to the spark plug (emphasizing TO THE PLUG (is the plug wet or have you tried spraying something like carburetor cleaner into the throttle body while cranking the engine?)). You need to verify that the spark plug is firing(emphasizing THE ACTUAL SPARK PLUG needs to fire in the cylinder). You need to verify that you have enough compression to ignite the fuel (a compression test). You need to verify that the spark plug is trying to ignite the fuel at the right time during the compression stroke (a timing test, a tad more difficult but needs to be done). If all the above is occuring correctly the engine will start. One of the above is not occuring correctly and that gives you a path to troubleshoot.
Sounds like you need a battery/electrical system test. A $20 test can usually pinpoint the problem and maybe its something simple like a loose or poor connection.
You should be able to test the horn circuit up to the steering column fairly simply without removing any major parts. If you do this first you can determine if the problem in in the steering wheel/column before you go through the trouble of removing the airbag. Also, a simple test with a quality scan tool and usually narrow down the problem quckly.
A diagnostic test of the transfer case system will reveal the problem. The system has both electrical and mechanical components that need to be tested. There is no easy way to test them without detailed information, a quality scan tool and a digital volt meter. The shift motor however has a fairly high failure rate.
It could be something simple like a U joint. Even if the joint is not loose, a lack of lubrication inside the joint can cause some nasty noises. The U joint is usually a sealed part from the factory and cannot be lubed. Removal of the driveshaft and inspection of the U joint can usually determine if the joint is bad.
Your vehicle uses a digital signal from a speed sensor on the transmission to the speedometer. Since you are not experiencing any other issues such as shifting (or check engine light?)my guess is you may have a bad speedometer. If you can verify that you are getting a "signal" from the speed sensor on the transmission to the speedometer on the instrument cluster then you probably have a faulty speedometer head. You would probably need at least a volt meter to check for the proper "signal" and removal of the instrument cluster may be necessary for proper testing.
You may need a heater core, however you MAY be able to flush the heater core and remove blockage. You could also have a problem with the "blend doors" that direct air through the heater core. Make sure your engine is running at its normal temperature as an overheating or underheating may indicate a different issue.
If the noise is present when turning the steering wheel and the vehicle is NOT moving, you may have power steering system noise or maybe even a strut bearing plate. Make sure you have adequate power steering fluid in the resevoir.
Most modern methods of coolant "flushing" are non intrusive and don't require cutting hoses as was done in the past, but it would depend on the equipment, the shop, and the person performing the service. Just the removing of sediment and maybe some sealers (while flushing) that were in the cooling system can "reveal" leaks. Some manufacturers that have factory installed coolant sealer recommend that a sealer be put back in the cooling system after a flush to prevent leaks. Bottom line is it depends on where the leak is as to what may have caused it.
Is the noise possibly coming from the lower portion of the steering column? The steering column intermediate shaft is a common source of popping noise when turning and driving over rough road surfaces. The shaft usually has to be replaced with an "updated" part to correct the condition.