Can we build computer without instruction pointer register (PC/IP)?
One possible thought could be a data-flow architecture. 

Here the various processing elements are wired together to implement the desired algorithm and rather than an IP register, each processing element (add, subtract, multiply, and, or, compare etc) acts when data is presented.

This sort of things is mostly seen today in fast algorithms embedded in FPGAs. I understand, but have no direct info, that crypto-currency miners are designed along these lines.

So, is this still a computer? Well. oddly enough, a popular way to program these machines uses "C" source code to describe what needs to be done and a sophisticated compiler to design the data-flow machine needed to get the job done.

On a similar note, the LabView programming environment presents a similar model with interconnected elements driven by the data and not an instruction address concept.