2003 blazer service 4 whd comes on I can't get it out of 4 whd

Google the OBD Codes

2003 GMC Yukon OBD Code P1571 & P1689

I pretty sure that what you'll want to look for is the body control module and from what my google-fu tells me it's located under the dash on the driver's side. Make sure it's not corroded.

My 01 Blazer had a similar issue and pretty soon would shift at all. I cleaned the heck out of it with QRC electronic cleaner and a dremel. A wire brush should do just as well.

Check vacuum canister on right side of
front axle and it's hoses ,for leaks

After that, go back to the transfer case shifter
vacuum sw

Remove the front axle vacuum actuator
& see if it is rusted, and not releasing the
right axle

2001 Chevy Blazer it likes to stay in 4 low. replaced sensor, pannel motor, older computern to check it was placed for a couple weeks or less it will do the same thing again. Just dies and quits has to be restarted agin still in 4 low . Tried to shift the gears slowly, Place in reverse and 2HD pressed and held while backing up this dinn't work either. To get it home I had to hold it in neutral and run the gears again ginally I got it to a shop. He is out of ideas too.

According to the diagnostic trouble trees for that code you need to replace the Transfer case control module.

The error that I'm showing for error code P1133 is 
P1133 Heated Oxygen Sensor (HO2S) insufficient switching bank 1 sensor 1(Rear Bank).  I would suggest having both of your Oxygen Sensors replaced if you haven't already had that done.  Hope this helps.  Thanks for an honest rating and for using FixYa.

check the fuses and wiring in the fuse box and the relay ,either that or the abs pump has a problem.

pull atc 25 amp fuse in underhood fuse center and 10 amp 4wd fuse inside cars fuse box,your problem is in control box behind kick panel on pass. side ,corrosion build up,

its the transmission, if it were the 4x4 not disengaging the vehicle would still move but in 4x4 mode.id get it to a shop if at all possible

Check the actuator (located under the battery plate). Remove the battery, then the plate, and you'll see something that looks like a horn attached to hoses. One side is soft, and may have a hole in it. This will cause the vacuum not to work, hence, your 4WD won't. Good luck!