Your old computer is an IBM Aptiva E2U running an AMD K6? Is the 256mb of PC133 SDRAM installed in the Aptiva? Or are you saying that is the kind of RAM the new computer uses? Or is your new computer the AMD K6? Just want to sure I know what you mean.
I had a hard time finding information on your PC at IBM's site (damn their forward-compatability website!

) but from what I can gather your IBM is running a Pentium II processor (could be wrong). RAM from that era can either be EDO DRAM DIMM's, EDO DRAM SIMM's, or PC66 SDRAM DIMM's (possibly even PC100 SDRAM DIMM's since 100mhz FSB was introduced late in the PII era, but unlikely).
Let me know some more information and I'll see what I can tell you. Make sure you're being specific -- RAM is specific as far as compatability. You have two seperate computers. Tell me the make and model (just like a car!

) of each computer and what processor is in which computer. Let's start with that. We'll take it from there after that.