I bought a house with a Bryant plus 80 heater. There was no thermostat so I connected the red and white wires (as I saw on one of your answers) to gat it fired up.

The burners ignited but flamed out in less than a minute and the led code showed #34 , (Ignition proving failure) but it did fire up and the main burners stayed on for acouple of minutes and failed again with the led showing # 31(which is Pressure draft safeguard) .

Could anyone of you shed some light on this please!

First, check draft fan and see if it works. It's probably a shaded pole motor that has two wires running to it, so you can ohm it out if you have to do so. Then, look at flame rod which is a little rod coming out of a white porcelain insulator like a spark plug. You want to clean this with some 1000-3000 grit sandpaper. This must be done from time to time. Electricity is conducted through flame to ground, so when it's dirty it does not work. The draft fans will seize up if not oiled. If it is a shaded pole motor remove fan and oil it. At each end there are felt pads that are supposed to be full of oil. If there are no oil holes then you need to make one at each end by drilling a 1/8" hole at the top of each reservoir. Use high-speed turbine oil available for $2.00 at any HVAC parts store in plastic bottle with long plastic tube. This oil is good for all motors in an ac/ heating system. You should also clean and oil your blower fan, too, because if it's dirty it will cut the airflow a lot causing the heater to shut off on the high-limit. Check all parts that will cause a loss in airflow like the filter and any cooling coils. Let us know how this works out for you.

Thanks. I'll let you know