LPG converted cars need special set up, it should start on petrol and only change to gas when operating temp. is reached so it is unlikely to be the problem.
The BRC system is a good one so as long as it is serviced and set up correctly it won't cause you problems. You have to have the best spark plugs in perfect condition for any car to run on LPG with the gap set at 0.9mm - 1mm MAX, all HT leads etc. must be in perfect condition as the system will draw slightly higher power from the coils due to the lower gap.
The IS needs valve seat wear protection, so if your valves have been damaged by not having the protection that could be the problem, look under your bonnet for a bottle of flashlube or similar?????
My advice is to check sparks, leads and starter motor then if you can't find a clear fault take it to an installer of BRC equipment, don't let "just anybody" service a LPG car. I have had an LPG car before and it gave nothing but hassle until it went to a competent fitter, who plugged it in to his laptop and solved all the problems.