Case-insensitive search in awk

Replace your expression to match a pattern (i.e. /&&&key word&&&/) by another expression explicitly using $0, the current line:

tolower($0) ~ /&&&key word&&&/

or

toupper($0) ~ /&&&KEY WORD&&&/

so you have

awk 'tolower($0) ~ /&&&key word&&&/ { p = ! p ; next }; p' text.txt

You need single quotes because of the $0, the BEGIN block can be removed as variables are initialised by default to "" or 0 on first use, and {print} is the default action, as mentioned in the comments below.

gawk has an IGNORECASE builtin variable, which, if set to nonzero, causes all string and regular expression comparisons to be case-insensitive. You could use that:

BEGIN{IGNORECASE=1}
/&&&key word&&&/ { foo bar baz }

etc. This is specific to gawk, though, but I find it to be more readable than the (more portable) alternative by meuh. Whether that's a problem is, of course, fully up to you.