Will RS 485 to RS 232 converter change the half duplex mode to full duplex mode?
No.  A converter merely changes the electrical signalling and gives you an explicit (typically modem control line reuse) or automatic (time based) control of the transmit enable.

Adaptation to a half-duplex scheme must be made by the software at each end.

As for why exactly your setup failed, that is impossible to answer with the limited information given, however it software not written with this mode of communication in mind could be a key part of the problem.