Thanks to @nina_kali_nina I've switched to using PCem instead of qemu since it does a better job replicating the experience I get on the T5200. I've been going through old and older distros trying to find one that has a kernel that boots on the emulated 386DX. So far it seems that no distro with a 2.x kernel will work. Newest so far is Slackware 2.3 with a 1.2.8 kernel. Bumping the RAM up to 32MB doesn't get 2.x kernels working either. Very strange.