In locking situations, it is rarely the BECM if the vehicle will start and drive.
I've had a stupidly lone day at work, and up in 7 hours for another stupidly long day at work - so I won't write more now.. but in short, as the others have said...
Earlier BECM's had a habit of burning the motors out on the front door latches - which then means they won't do anything when the central locking is triggered, either by the key in the door, (though the drivers one will operate, as it's a mechanical linkage), the sill lock button on the door card (again, except the one you manually actuate, as it's a mechanical linkage) or the remote.
Later BECM's has some form of update in the firmware that stopped them from triggering the locks all the time, but being a '97, yours is probably previous to that.
Don't go buying a whole BECM lockset and all that - a) you're wasting your money as it's unlikely to be a BECM problem and b) randomly swapping a BECM/lockset usually ends up causing other sets of problems/headaches, either straight away or in the future.
Pete has already posted the link to my door latch tests... do them first, and then you know what you've actually working with. My best guess... both front door latches have burnt out motors, and probably the drivers CDL switch is faulty, as this will trigger when the drivers door is opened (either with the key and the BECM will recognise this and unlock the other doors or the remote). The tailgate locking is controlled via the drivers CDL switch too - so if the latch is even unlocked but the switch is faulty, the BECM won't necessarily recognise it's been unlocked, which can cause starting issues, and as a separate circuit, the tailgate won't open.
If your latches are burnt out - and you've already replaced them - then I would be disconnecting the RF receiver antenna as a start aswell - I've heard of people going through 3 or 4 sets of brand new latches because they haven't sorted the RF issue, which is the root cause of the problem. The best option is the MKIII receiver. For a '97, the second best option is probably a MKII receiver from a '99 (ish) onwards vehicle and disconnecting the antenna wire.
Hope this helps,
Marty