array formulas with AND statement

I've asked a similar question before, but I need more help.
I have a conditional statement such as:
=SUM(IF(ABS(B2000-B1000:B3000)<2,1,0)
this will find all the instances where the difference between B2000 and a cell between B1000 and B30000 is less than 2,
and add up the number of times that is true.

This works fine when I enter it as an array formula.
Here is my problem: I want it to satisfy conditions in 2 columns simultaneously, and only only return TRUE when the
conditions are met in both columns. So, I if B2000-B2340 is less than 2, but C2000-C2340 is greater than 2 (or any
number that I set), it is false. But if B2000-B1245 is less than 2 and C2000-C1245 is less than 2, we get a TRUE
result.

I tried =SUM(IF(AND(ABS(B2000-B1000:B3000)<2, ABS(C2000-C1000:C3000)<2),1,0)
but it didn't work, even entered as an array formula (I got a FALSE, ie 0, even when I knew it to be true). Obviously
the problem is with the AND statement. Can I make certain both parts of the AND are entered as an array?

-David