Hi, srmarchi!
As You mentioned, that You are new to Linux, I assume, that You wrote the TinyCore to SD card using Windows? Is there an option to write CD disk? What versions (TinyCore, TinyCorePLus, Core) have You tried?
By the way, there are even earlier versions, for example 4.7.7. Your machine is quite aged, so why not to try.
Good luck!