The tce folders (tce, tce32, tce64, etc) and everything in them should be owned by tc:staff.
Just to be sure it's understood, tce=tce32 or tce=sda5/tce32 are telling tinycore which tce folder to use and are not telling it to boot a 32-bit version of tinycore.
Which Xserver are you trying to use - Xvesa (32-bit only), Xfbdev or Xorg-7.7?