Solution needed for counting pulse inputs WITHOUT using Intterupts

That's just poor programming.

First of all: why would you even want to disable interrupts for an extended period?
Secondly: if you want to disable a specific interrupt, do that.

In most programs, the only reason to use noInterrupts() is to copy a value that is updated by an ISR to a new variable, after which interrupts() is called switching all interrupts back on.