The test register actually sets up 3 tests, alpha test/destination test/depth test, which are all done in order if all 3 are enabled. If a pixel fails the first test, it doesn't pass the others. The depth test probably isn't needed for your app, so I'll explain the first two.
Here's an example that sets up a test where pixels with an alpha value of 0 will fail and no buffers are updated for failed pixels. I included available settings after the values. The AFAIL setting determines what to update with the failed pixel.
This test sets up whether the pixels destination alpha value passes. This test changes depending on storage mode. 16-bit alpha is either 0/1. 32-bit alpha requires it to be >= 0x80. Automatic pass for other modes.
gsGlobal->Test->ATE = 1 // enable
gsGlobal->Test->ATST = 7 // not equal, (never,always,<,<=,=,>=,>,!=)
gsGlobal->Test->AREF = 0x00 // comparison alpha value
gsGlobal->Test->AFAIL = 0 // keep, (keep,framebuffer,zbuffer,RGBA32->RGB32)
gsKit_init_screen() sets up the alpha blending registers to 0x01 or GS_BLEND_BACK2FRONT by default, which just sets A to 1 (framebuffer). Assuming there are no random bits being set, that would set the algorithm as (destination-source)*source_alpha>>7 + source. Maybe the alpha values in your texture prevents it from drawing?
gsGlobal->Test->DATE = 1 // enable
gsGlobal->Test->DATM = 1 // pass if 1
Also, the PrimAlpha setting in gsGlobal needs to be set with GS_SETTING_ON or GS_SETTING_OFF as that controls whether the texture colors will have an alpha value when drawing.
For the resolution setting, for PAL, you need to set the width to a factor of 2560 and the height to a multiple of 256. The lowest resolution would be 256x256 since 256 is a factor of 2560 and 256 is a multiple of 256. The display register causes this type of of complexity in order to allow more flexible drawbuffer sizes/resolutions combinations to be set.
I think that pretty much sums that up. There's more that could go wrong, when multiple queues are involved. gsKit introduces a lot of complexity into a somewhat simple system, heh.