AN M20P PLT; AFTER LNDG AT HWD; FAILED TO CONTACT GND CTL BEFORE TAXIING ON THE PARALLEL TXWY.

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HAD JUST COMPLETED GPS APCH TO RWY 28L AT HWD. AS I TAXIED CLR OF RWY 28L; HWD TWR CLRED ME TO CROSS RWY 28R AND TO CONTACT GND ON '.4.' AS I WAS XING RWY 28R; TWR ASKED IF I WAS STILL UP ON HIS FREQ. WHEN I RESPONDED 'AFFIRMATIVE;' TWR ASKED ME IF HE SHOULD INCREASE THE RWY LIGHTING FROM MEDIUM TO HIGH INTENSITY. I RESPONDED THAT HE SHOULD; AS I HAD NOT SEEN THE LIGHTS UNTIL AFTER I SAW THE RWY AT ABOUT 2 MI OUT. ALL THE WHILE I WAS ENGAGED IN THE CONVERSATION WITH TWR; I CONTINUED TO TAXI ACROSS RWY 28R AND ONTO TXWY A (MAJOR PARALLEL TXWY). AS I WAS SWITCHING FREQS TO GND; I SAW A CHEROKEE ARROW APCHING FROM MY L; ABOUT 200 FT AWAY. NOT WANTING TO TOP IN THE ARROW'S PATH; I CONTINUED ACROSS TXWY A TO THE FAR SIDE OUT OF THE WAY BY THAT TIME; I WAS UP ON GND FREQ. GND WAS INSTRUCTING THE ARROW TO STAY TO THE R AND THAT GND WAS NOT TALKING TO ME. I THEN CALLED GND; TOLD HER I HAD THE CHEROKEE IN SIGHT; AND APOLOGIZED FOR MY ERROR. I ALLOWED MYSELF TO BE DISTR BY TWR'S REQUEST. SHOULD HAVE WAITED UNTIL I WAS STOPPED; SHORT OF TXWY A; BEFORE ENGAGING IN ADDITIONAL CONVERSATION.