I have a 96 Ulysse as well with the keypad.
Remove the keypad so that you can get to the connector and wires behind it. These wires can wear and break. Hopefully this is your problem. If so, repair the wires. If this is not the case you could get hold of another keypad. Their are loads around as citreon and peugeot used them as well from 1996 to around 1999. Also Ebay often have them for sale.
When you get the green light to come on, start your car and then unplug the connector from the back of the keypad. You must have your engine running while you unplug.
By doing this, the car will start without using the keypad.
I have unplugged mine and I have had no problems starting.
Hope this helps.