I bought a truvativ elita crank and gxp bottom bracket to replace my old shimano sora crankset. I removed the old crankset with no issues.

I began installing the gxp bb. I screwed in the drive-side bearing cup. Then I went to start the non-drive side cup and it wasn't catching any threads. I looked in there and it appears as though the protective tube has lodged itself in the bb shell. It is sticking too far through for me to start the other bearing cup, and when I removed the driveside bearing cup, the tube did not come out with it.

Any suggestions on what to do?

If you have both cups out, you should be able to just push the tube out. The tube is just there to seal the BB from crud and water that might run down the frame tubes to that area.

that's what I thought, but it isn't coming out. it's stuck in there. should it be able to push through both sides?

Is the tube from your old bb? It may be stuck in there by gunk. What standard was the old bb?

hmmm...I think it may be the old tube that caused it to do this. not sure what you mean by standard, but it was a shimano bb-un40 according to bikepedia

Hmmm, you have a picture? Are you saying you jammed the new tube inside the old tube?

I was able to use a socket as a punch to remove the tube, but now that I can look into the bb shell, I can see what appears to be a sleeve on the non-drive side of the shell. When I was removing the old bb, the cup that I removed from the nds unscrewed fine but was cracked and fell apart once out. Could it be the cup that was supposed to unscrew that is still in the bb?

and yes, after getting into better light, I am aware that I need to do a waaaay better job of cleaning

Yeah, that's what it looks like, the threads go deeper than where that piece is sitting which is why you couldn't get the new bb cup to seat. Not sure about how to remove it though

awesome!

should have let the lbs have at it

OK, what you likely have stuck in there is the plastic non-drive side cup that Shimano uses for many of it's older square taper cartridge bottom brackets. If you remove the non-drive side cup first, the plastic ones often fracture and leave a large part still in the bb threads. You can guess how I know this.

Removal requires a lot of CAREFUL work to slot and break out the remains without damaging the threads. If you aren't comfortable doing this, a trip to the LBS is highly recommended.

ahhh, lesson learned. I ended up swinging by the bike shop. 15 minutes and $10 later, all is well
I was able to install everything else with ease.