Can anyone in the community clarify for me the following:
How does one correctly decide if a computer is compatible with gcc7.2 or gcc4.9? In my case, my Intel486 Laptop works great with gcc4.9. However, it does not work with gcc7.2. In contrast, my Ubuntu desktop PC works great with gcc7.2.
Most likely because your 486 is incredibly old... and perhaps your Ubuntu desktop PC is a newer chip? Possibly pentium class or higher?

Without knowing the specifics of your pc, it's difficult to answer. In any case, I've not found a definitive list of cpu/gcc version compatibility.
Also what does the acronym "NOASM" represent? I understand GCC (GNU Compiler Collection) is a compiler system produced by the GNU Project supporting various programming languages. However, Google could not identify for me what is the meaning of "NOASM".
It isn't "NOASM"... it's "No ASM"... as in "no inline assembly language".
Inline ASM offers some performance benefits and coding shortcuts, but comes with some caveats... like CPU incompatibilities etc.I would think that using various "-m options" could impact on things as well:
https://gcc.gnu.org/onlinedocs/gcc/x86-Options.htmlIf the person compiling the application has enabled various instruction set extensions that are not supported by your particular CPU.