|"I want to remove the RAM cards from the E Machine and transfer the data to my new computer"|
There is no "data" held on ram cards. The data is all contained in hard drives.
You may be able to remove the drive from the dead Emachine and slave it into your new PC to retrieve documents, pictures, music & video files etc. Installed programs from the Emachine will not run in the new system. Those kind of things will have to be re-installed.
Goin' Fishin' (Some day)