Petaflop K Computer Fastest on Earth

No, computer processing speed is mostly irrelevant to internet bandwidth. In-fact, it's mostly irrelevant to a PCs over all performance. That the central processing unit (CPU) can perform many quadrillion flops per second is irrelevant if the North Bridge is not capable of buffering at the same speed. If the bands leading from the peripheral components interfaces (PCI slots) or advanced graphics ports (AGP) is slow then the processor will process information fast, but will bottle-neck at the South Bridge. A new MB architecture would be required, the AT form-factor with its typical bus speeds would not allow for much performance increase. Also you would need to make sure your Network Interface Card (NIC) is top of the line and operating at 1GB/s or greater. Gigabit Ethernet NICs are becoming more common, but I personally am running a 100 Base-TX network with only a 10/100 full-duplex NIC.

*gasps* So much porn....

"I wonder if this kind of computer power would help with my terrible internet connection."

I think that all the time. It usually doesn't help. The K computer on dialup is still just a computer with aol v.1.