Not sure if I'm missing something, but COUNTIF should work.

=COUNTIF(A:A,"1990") gave me 5

If you want the sum for 1990 use:

=SUMIF(A:A,1990,B:B) which gave me 41,484

Those aren't dates formated to look like years are they? Example:
real value is 1/1/1990 but shows up as "1990" due to formatting. If
so you need to change the formula to look for the whole date not just
the year.

HTH,
Steve Hieb