DeVry eSoc Max 7000

The speed grade designation on the outside of the part -6 or -15 is not part of the internal device IDCODE. MAX+PLUS II or Quartus cannot tell which speed grade it is and they don't care -- the speed grade doesn't change functionality of the features or of what you program into the part. When you auto-detect, it should only be able to tell you that its a EPM7128S. It won't know the package or the speed grade because those are irrelevant. Quartus will use JTAG IDCODE to determine if its 7128S, 7256S, 7064S, etc.

For programming step, the ID process is different. There is an ID on the part specifcally for programming identification so the tool knows how to program the part. There have been several die's for 7128S and each would be programmed differently. If the tool can't read this silicon ID or says it is not recognized, either the ID got erased somehow through corruption or the tool does not have the algorithm to program what may be a very old version of the silicon.

For a device this old, I would rely on MAX+PLUS II. If it can't program it, its possible the device is bad.