Engine control light, Kat broken or not ??

good day,I’ve been driving a V6 3.2 Phaeton bj 10/2003 with 110 tsd km the vehicle has full equipment and I’m thrilled! I bought it privately for only 8000,- € with the defect that the pre-kat is broken and board battery needs to be replaced… after visiting and driving it was clear that the kat can not be broken, since there is no clapping to hear and no loss of performance…and kats usually do not break. AU/HU to May 2013 get with defective ?! after 6 weeks after the purchase the engine control light went off by itself and since yesterday the lights up again, maybe the lamba probes ?? and my tire pressure control does not work,if I turn it on it and stands system malfunction maybe someone can help me mfg tamer