I went to the extent of resoldering virtually every connection on the circuit board, and there still seems to be a problem with an intermittent connection somewhere on the board. If I put pressure on any of the plugs into the board, I can get the heater to come on. It may continue work for an hour or a couple of days.
I found this information on the internet: "Bulletin United Carrier Corporation Technologies Carrier Residential Engineering SMB 96-0023 Subject: FURNACE CONTROL BOARD RESISTOR SOLDER JOINT FAILURES 04/17/96 UNITS AFFECTED: CAC: 58MXA, 58MCA, 58WAV, 58PAV, 58RAV BDP: 350MAV, 340MAV, 395CAV, 376CAV, 383KAV, 373LAV PAYNE: 480BAV, 481BAV, 490AAV Resco/Eventemp/Cobra: GB1AAV, GB3AAV SITUATION: A resistor solder joint failure mode has been identified on the following control boards used in the subject gas furnace. Affected Controls: HK42FZ004 (Obsolete) HK42FZ007 (Obsolete) HK42FZ008 (RCD Replacement) HK42FZ009 (Production, Open faced control board) HK42FZ011 (Production, Covered control board) Refer to Table 1 for the affected serial number ranges of the subject units. Table 1 CAC MODELS SERIAL NO. RANGE BDB MODELS SERIAL NO. RANGE 58MCA 3193A - 4595A 340MAV 3193A - 4595A 58MXA 3193A - 4595A 350MAV 3193A - 4595A 58PAV 1594A - 4595A 383KAV 1594A - 4595A 58RAV 1594A - 4595A 373LAV 1594A - 4595A 58WAV 1594A - 4595A 395CAV 1594A - 4595A 58ZAV 1594A - 4595A 376CAV 1594A - 4595A PAYNE MODELS SERIAL NO. RANGE RESCO/EVENTEMP SERIAL NO. RANGE /COBRA 480BAV 1594A - 4595A GB1AAV 1594A - 4595A 481BAV 1594A - 4595A GB3AAV 1594A - 4595A. For further information on replacing these controls please contact your supplier."
I plan on finding an HK42FZ016 board to replace my HK42FZ004 board (I have a 350MAV model furnace) and hopefully that should fix the problem. This might be the same problem other people with Payne, Bryant and Carrier furnaces that are reporting on this bulletin board. I hope this can help someone else.