I have a stuck transfer shift 03 montero sport.

Sounds like there is an issue with your transfer case , most of the time related to a bad electronic solenoid.

Needs ****** fluid top up OR TPS throttle position adjustment.

1. • 1 Start your Dodge truck's engine.
     
   • 2 Turn the electronic transfer case from "2WD" to "4WD Lock" to engage the high range 4WD, if the dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" to "4H." The electronic transfer case is located on the instrument panel and is marked with "2WD," "4WD Lock" and 4WD Low." The lever-equipped transfer case is located to the right of your leg and is marked with "2H," "4H" and "4L."
     
   • 3 Shift the transmission into "Neutral" while the vehicle is either stopped or rolling at 2 to 3 mph to begin engaging in the low range 4WD. Turn the electronic transfer case to "4WD Low," if the Dodge truck is equipped with an electronic transfer case; otherwise, shift the transfer case lever from "2H" or "4H" to "4L."
     
   Tips & Warnings
   • Indicator lights will come on and alert you that your vehicle is in either the high or low range of 4WD.
     
   • Do not engage in the low range of 4WD drive if the transmission is in gear; you must shift to "Neutral" first.
     
   • Many Dodge trucks allow you to shift from 2-wheel drive to the high range of 4WD at up to 55 mph--consult your truck's manual to ensure that this is possible. Do not exceed 55 mph while engaged in the high range of 4WD. Do not exceed 25 mph while engaged in the low range of 4WD.
     
   • Do not engage in 4WD unless you are on slipper or rocky roads.
     

Find one at the dealer, you may want the Transfer Case Cable

Mine did the same thing so I removed the center console and then the boot around transfer case shifter and the shifter it self.
This is when I discovered a broken linkage that had wedged itself between the 4L & 4H shafts in the transfer case. I removed the broken parts and reassembled and it will shift between 2H & 4H but not 4L until the broken plastic linkage is replaced. Found your post while lookin for the replacement part so I thought I would try to help. Good Luck

is it true that I have to put my montero in reverse to engage 4 wheel drive first?

The transfer case is stuck in the low range. If manual shift try shifting from low to high several times to see if free up. If electronic, check all fuses and make sure you hear transfer case change range. Do this by shifting with key on engine off. If no change refer to qualified transmission mechanic.

Bad 4wd position sensor located on transfer case or bad sensor located on right front axle housing for 4wd engagement position.

It's either the sensor on the top of the transfer case, or the one on the front diff. Look here, scroll down to about the third post.

http://msport97.proboards.com/index.cgi?board=faq&action=display&thread=6258

This was a weakness of the Montero Sport models. If you google Montero Sport 4WD light flashing you will find lots of information. The best troubleshooting article I have found is here: http://4wd.blogeasy.com/article.view.run?articleID=318776 This article is about the Pajero, but the Montero Sport uses the same platform so this article applies.

The Montero Sport uses several switches and vacuum modules to put the system in and out of 4WD. If any of these malfunction, the light may flash continuously, flash intermittently, fail to come on, and it can trigger the anti-lock brake light to come on. In brief, if the 4WD shift lever is engaged, but the transfer case doesn't engage, the sensors show a mismatch and will cause the light to act funny including triggering the vehicle's anti-lock break light. These SUV's need to be shifted into 4WD regularly to keep the switches and mechanisms working correctly.

Try this before you even think about a visit to the $$$$$ Mitsubishi Dealer:
Shift the 4WD lever between 4WD High, Low and 2WD at least 100 times. Often, this will free the mechanisms and resolve the problem. It worked for me after three years of trying everything else including the dealer replacing switches, etc. If this does fix it for you, just be sure to shift the vehicle in and out of 4WD several times at least one a week and this will keep the mechanisms lubricated and functioning correctly. If that doesn't work, try the above link (article). Good luck!

Jeff