What Honda Rodeo has the same front driveshaft as Isuzu Trooper?

The key lock cylinder operates the ignition switch sometimes ignition switch is separate sorry I didn't find where ignition switch is located if the lock cylinder is plugged into it.
You should have a starter relay and starter relay fuse.
This diagram of starter circuit shows the clutch pedal switch in the circuit on an automatic should have the neutral safety switch in the circuit. This is for 95 Rodeo.
Stater Motor Circuit Diagram (1995-1997 2.6L Isuzu Rodeo) (easyautodiagnostics.com)

How do I remove the key ignition cylinder? ' Isuzu SUV Forum (planetisuzoo.com)
Isuzu Trooper Ignition Switch Replacement ' Cost & Service ' RepairSmith
Changing the Ignition Lock: Changing the Ignition Lock, Safley ... (2carpros.com)
Starter and solenoid
Isuzu Trooper Starter replace under 1 Hour - YouTube
Isuzu Trooper (1995 - 1996) - fuse box diagram - Auto Genius
Starting System & Wiring Diagram - YouTube

Probably BUT what about the CONTROL MODULE. There are a lot a lot of electronics involved!

Crystal, this is what I found on the Rodeo starter fuse/relay.
Check the attached links,instruction and guides, Good luck
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Honda rodeo . They share same frame.

check the u-joints in the drive shaft. With engine off and shifter in park with e-brake engaged Climb under truck and locate driveshaft Try turning the driveshaft back and forth normally shaft will move about 1/4 inch while turning shaf, look at u-joints both front and rear for wear.

no.

I worked at Dealership which sold these things new. The transmission is notoriously weak...have a transmission shop you trust check it out. I have rebuilt a few of those transmissions,and overdrive is usually the first thing to let go.Don't drive it for long:the contamination running thru the trans.will cause more damage,add to the repair and leave you stranded somewhere.Sorry but I don't think you are getting away cheaplyThe Honda Passport is a Rodeo with a Honda grille.you can still buy some Isuzu mechanical stuff thru Honda stores.Good luck

Go to my profile I have just explained how to change a cv boot on a Trooper. The axle needs to be taken out to change the boot so the same solution. What you call an axle I have refered to as a drive (short for driveshaft) It takes a lot of explaining so save me a lot of writing if you read the solution I gave for changing the CV boot. Cheer's

not transfer case motor....there is none on a rodeo....trooper has torque on demand.....rodeo problem is likely shift on fly mtr...mounted on front axle....if u dont use 4wd regularly it sticks and gets stuck.