ok now we know the make of boiler.which is probely the best modal ideal ever made forget the display & board issue. still recamend engineer inspect it though. how have you confurmed that the con pipe has fully been defrosted
with no display on the ctrl pannel my guess it that water has leaked from the sump and blown the pcb. ? have you got power at the switch. recamend you go on the gassafe website to fond a local engineer.
this has been a problem since installation, could be possible reverse circulation when running hw feel the cold mains pipe going into the boiler for a rise in temp to confirm
Go to the gassafe web sit to get a qualefied heating engineer to remove the low water pressure switch and clean/replace it. may as well have serviced at the same time.
also with pre heat, if there is a dripping tap, the boiler will come on more often , should be aprox 1.30hr for the pre heat, and about 20 sec to heat hot water storage
an inhibitor is a neutralisar . not a sludge remover. once you have cleaded the system with a quality product such as fernox or sentanel.x800 then you can add an inhibitor.
At the same time you might consider employing an engineer to cemicaly clean the system, look up the gas safe web site. there you will get a list of your closest engineers. bit late in the day though. it will take the plastera half a day to prepaire so you might have time.