Patrick McDonald wrote...
....
I have two columns of values ("E" is 480 rows and "J" is 2200 rows).
Some values in E appear in J; this I've verified using <ctrl+<f. For
each row in E, I am entering
=SEARCH(E5, J$5:J$2238)
to simply result in a 1 if there's a match and #VALUE if not. In
another column I am using =IF(ISERROR(K5), "new", "existing") to
determine my result so I am expecting _some_ #VALUEs.

The formula =SEARCH(E5,J$5:J$2238) very likely doesn't do what you seem
to believe it does. SEARCH returns the first/leftmost position of its
1st argument in its 2nd argument, both interpretted as strings. If you
pass it a range or array 2nd argument, it returns an array containing
the positions of its 1st argument in each of the items in its 2nd
argument. It looks like you want

=MATCH(E5,J$5:J$2238,0)

instead. You should then replace the ISERROR in your second formula
with ISNA.

I've entered the formula using <enter and the array method
<ctrl+<shift+<enter.

Regardless of the entry method or formatting (general, text, number), I
am getting #VALUE in every row, including rows where the value in E
_does_ appear in J$5:J$2238.

If all of your formulas really do look like

E#:
=SEARCH(E#,J$5:J$2238)

then if you're entering each & every such formula in a single cell,
each & every such formula is returning the *same* result as if you had
used

E#:
=SEARCH(E#,J$5)

As I said above, it appears you need to use MATCH rather than SEARCH.