Hi mate,
your System is like mine. AMD Athlon DualCore 2500+, 4GB RAM, ATI RADEON HD 6850 1GB. Windows 7 Pro (32 bit).
I have the same Problem like yours. And there is nothing to do except to buy a new PC because I think a Dual Core is nearly historical. That's true!
I can't play the first Round always dying so quick because of the lags. I know what you mean the screen freezes for 5-10 seconds. There seems to be loading the animation or something like that in the 1st Round of every match.
I'm sorry but it seems we can nothing do about it, as I said before except to buy a new HIGH-END PC.