elsif ($^O eq "Linux") {
    eval { require Term::ANSIColor; };
}
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is useless. You're using the functions from Term::ANSIScreen instead of those from Term::ANSIColor. Term::ANSIColor is a subset of Term::ANSIScreen, not the non-Windows equivalent of Win32::Console::ANSI.

Furthermore, you can simplify your program using the if pragma:

# Load ANSI driver if running in Windows.
use if $^O eq 'MSWin32', 'Win32::Console::ANSI';

use Term::ANSIScreen qw/:color :cursor :screen :keyboard/;

...
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Using the simpler code shouldn't fix anything, but since it will load Win32::Console::ANSI at compile time as if you had said use Win32::Console::ANSI;, it might.

Update: Added missing quotes as per reply.