Subaru automatic transmission

Is your 2003 Subaru Outback automatic or manual transmission?
If it is automatic, then your transmission sounds like it's malfunctioning into the reverse gear as it is not aligning properly.
If it is manual, then your transmission sounds like it may have a bad clutch or bad reverse gear.
Either solution is not cheap. Good luck.

SUBARU Automatic Transmission Solenoid A Dropping Resistor July 2, 2011. Author: Lewis Werner The SUBARU automatic transmission dropping resistor is connected in parallel with duty solenoid A. Duty solenoid A regulates the Subaru automatic transmission fluid line pressure. Like most of the transmission solenoids, duty solenoid A's duty cycle is varied by the transmission control unit (TCU) to control the line pressure.
The dropping resistor works with duty solenoid A in regulating the automatic transmission fluid line pressure. This resistor keeps a certain amount of current flow through duty solenoid A during the 'OFF' portion of its duty cycle. So in other words, duty solenoid A is never fully 'OFF'.
The dropping resistor is located on the right front shock tower, near the MPI (multi-port injection) fuel system dropping resistor. The photos at the right depict the Subaru automatic transmission dropping resistor.
If this resistor fails open, becomes disconnected, or has its wiring severed, one result might be increased shift shock. The reasoning behind this is that without the resistor in the circuit, the line pressure may be higher, since without the current passing through solenoid A during the 'OFF' portion of its duty cycle, it will tend to close further, and thus not bleed off as much pressure from the automatic transmission fluid pump.
If the resistor fails open or is disconnected, it should cause the ATF temperature lamp to flash 16 times on the next startup, since the TCU would be able to see electrically that the resistor is open.
This resistor was used on the SUBARU 4EAT phase I and 4EAT phase II automatic transmissions. It may also be used on the 5EAT though I have not confirmed it. http://www.scoobyenthusiast.com/subaru-components/subaru-automatic-transmission-solenoid-dropping-resistor

Your transmission slips ---your done,there is
only one fix,remove it & have it rebuilt or
a reman installed

I'm afraid adjusting the bands on an automatic isn't a home mechanics job. No movement at all is more than just band adjustment. It sounds more like no fluid or no fluid pressure. Did you check the transmission fluid level? Remember to check it when the car is running with a cleaned off dipstick. Also, there is a screw on filter on the outside of the transmission that changes very easily, just like an oil filter. If that has never been changed on your '96 it may well be clogged, restricting or halting the fluid flow. If you change it, remember to top off the fluid in the transmission after.

Could either be your shifting linkage needs to be adjusted or your transmission solenoids need to be replaced

Sounds like the clutches for 3rd Gear are worn out. Need to rebuild or replace the transmission.

First off before adjusting anything change your tranny fluid and filter that usualy helps the tranny

It is on the left side hard to spot. Look below the heater hoses. Good luck, take your time and have a great day.

Try replacing the transmission filter and the trannie fluid. Mine would only go in reverse, and now it drives pretty well. This year has a screw on filter. Hope this helps

Check the transmission fluid level. If it is low, fill it. Otherwise, if you happen to have a Subaru Select Monitor or equivalent, then you can read the fault codes for the 4EAT transmission and it will tell you which internal solenoid valves are sticky. At that point you can either add a quart of stuff that says it solves transmission problems and hope for the best, disassemble the transmission and change the problem valves, swap the transmission for one that works, or take it to someone to have it repaired.