I was looking to purchase a new PC, but i figured i would just try to upgrade my current one (DIY Project).
Looking through my system information to see which hardware was good enough to keep and saw:
Processor: 2x Intel(R) Pentium(R) D CPU 2.80GHz
How would you calculate your processing power:
Is it 5.60GHz?
Can it handle programs that require 3.00+GHz?

No, it doesn't calculate as 5.60GHz. Dual Core allows for multitasking.

Dual Core processors both work at the same speed, in your case 2.8GHz. If you could imagine having a chopping knife in each hand, and you could chop with both at the same speed, then one hand would be chopping carrots while the other is chopping Onions.
You would need something to feed the carrot to your left hand, and something to feed the onion to your right hand, allowing the two hands to work independently.

Your processor has two cores, and to function at optimum they would need memory space; described as dual channel, dedicated in a relative sense, to each core - feeding each core the data it will process.

But, the operating system and software need to be capable of utilising this architecture to benefit from it fully - and your memory must be duel channel.

soo if the program says it needs pentium 4 3.0 , and your pc is pentium D then you can run the 3.0Mhz needed program. But the program asks for Pentium D or Dual core 3.0 , then you can't. (can't means, you sill can run the program but it will be slow. It is not that it is impossible).

When making comparisons like this you have got to take into account the performance of the rest of your system, never base performance on just the CPU alone. A Pentium D processor will not fit into a Pentium 4 motherboard.

As you are pondering the virtues of two low-end processors, why not wait a little longer until the better kit comes down in price? While you are waiting you could be gradually making your PC fund increase.

Please consider these comparisons:

Pentium D 2.8GHz

Pentium 4 3.0GHz

Here, both the above CPU's are charted together, see the bottom two.

I also got some Benchmarks from here. I set it up with the comparison you suggested, but there was no way of posting it here. But I'm sure it won't be a problem for you to enter the details.