1) i have an old disfunctional programmer for 89C51 which works through computer serial port, i have found that the RESET pin in the programmer is always kept high. is this the problem?
Sounds like a candidate for the trashbin. With the event of ISP chips such as the P89C51Rx2 or P89C66x or the JTAG chips from Cygnal you do not need a programmer. Anyhow "an old disfunctional programmer " will not have the setup for modern derivatives unless a software update is available.
2) want to know how one can make out if the microcontroller is running? because i dont know how to make out if it is software problem or hardware problem.

The simple way is with a scope, if you do not have one such several methods exist, a couple of suggestions.
1) upload 'blinky' and install a LED
2) toggle a port pin in the workloop, and measure with a voltmeterthe voltage should be 1/2 Vcc when the processor is running.

Erik