You are reading the very first line, but you don't do anything with it.
I think you should also indent your code, so you see your mistakes like no EndIf.
I think it is good habit closing opened files:
Close(3)
I reformatted your code a bit and put two remarks in it.
Break ON
DIM $csv,$bal,$csv_array,$read,$controlnum,$line,$x
RedirectOutput("C:\temp\output.txt",1)

$csv="C:\temp\test.csv"
If Open(3,$csv) = 0
    $read=ReadLine(3)
    While @ERROR = 0
        $read=ReadLine(3) ;This should be placed just before the loop
        $csv_array=Split($read,"|")
        If UBound($csv_array)

            ;Add together first balances
            ? "Account:  " + ($csv_array[5]) + "   Balance:   " + ($csv_array[71])
            $cintndc = Round($csv_array[66],2)
            $balsndc = $balsndc + $cintndc
            ;$balsndc ?

            ;add together second balances
            $cintproc = Round($csv_array[71],2)
            $balsproc = $balsproc + $cintproc
            ;$balsproc ?

        Else ;This Else is redundant
        EndIf
    Loop

    @CRLF

    ;add together first and second balances
    $total = $balsndc + $balsproc
    "Total balance is: " + $total ?


    $read = Close(3)

    RedirectOutput("")