Is there any way to make the computer process more keyboard presses at the same time?

Use a ps2 keyboard

 

... Since when does playstation 2 has a keyboard attached to it...?

 

Ps2 is an older port type that was common during the late 90s and early 2000s. Many gaming motherboards still retain the port because it's a little faster than USB and can handle more than 7 keys pressed at once. It's a round port, usually colored purple for keyboards and green for mice. It will usually be located towards the top of the motherboard, like above the other ports.

Technically it is slower than USB, but it's hard wired into motherboards and not reliant on driver like USB is.

 

I don't think my laptop has any way of connecting to this kind of device, and I don't think they're even sold anymore.