There are a few reasons for this. Do you know if your old transfer case is a post-1983 model? Also, is your W56 a W56-C/D/ or E (
what's that?) and is your t/case a forwarding shifting style transfer case from a carbureted truck?
If it is a post-1983 model, make sure that both snap rings of both the input and counter shaft bearings are able to rest flush against the face of the transfer case front reduction housing. If they are not, then slowly rotate the input shaft while applying pressure with your free hand on each bearing. They will suddenly reposition with both snap rings in contact with the front housing.
The reason for this is that starting in 1984 Toyota redesigned the large gear on the counter shaft as well as the low speed idler gear to incorporate what we refer to as a "Run Quiet" design. These late mode gears have a thin sheet-metal-like pre-loaded gear plate that mounts directly & coaxially to each respective gear. Each thin gear plate (two in total) has exactly one less tooth count than the gear it is mounted directly onto. Therefore, there is only a specific area around the perimeter of each gear where the tooth of its mating gear lines up "in time" without interference. What happens is that while the gears are in mesh, the opposing gear forces this gear plate to rotate at a higher speed, as it has one less tooth, and because it is pre-loaded, it requires a minimum amount of force to remain in mesh. The result is that the teeth in contact are forever pre-loaded so that there is no noise from gear chatter (zero backlash). Hence they
run quietly.
What typically happens is that one gear, for instance the input, is pulled out of the case in such a position that it is only in mesh with its opposing gear (and not also its gear plate). If the gears are then rotated like so without also remaining "in time" with the pre-loaded gear plate, then the teeth of the input will never allow the input itself to seat in proper position where it's bearing's snap ring is flush against the front of the transfer case, and any attempts at installing the transfer case behind the transmission will only result in difficultly and eventual damage to one -or both- "run quiet" gear plates. The trick in this case, as mentioned above, would be to slowly rotate the input shaft while applying pressure with your free hand on each bearing. Then, as each gear rotates and finds the specific area that is "in time" with the pre-loaded gear plate, the gear will suddenly fall into its correct position relative to the front reduction housing.
Another issue could be that you are trying to install a transfer case that came off the back of a 1979 L43 4-speed transmission. Yes the spline count and diameter are the same, but these early transmissions did not have an internal means of limiting the position of the output shaft and instead relied on a spline stepping of the transfer case's input gear to hold their output shaft in place. This was done away with on all transmissions L45 and newer, and as a result of a redesigned output coupler, interfere with the L43 type transfer case input. If this is the case for you, then the solution is simply to grind down and round the spline stepping until it clears and fits into the updated output coupler design used in your W56 transmission.
Take a look at our Transfer Case Bible, there is a lot to learn and it's a lot of fun!
http://www.marlincrawler.com/tech/transfercase/transfer-case-biblePost some pictures and some additional information and we'll go from there. The most important thing right now is to NOT force the transfer case in place. The t/case should naturally slide into position with little effort. If there is a half inch or quarter inch gap, then an incompatibility is present and forcing the gap shut will only result in damaged parts.
Regards,
BigMike
