Sure they can. There several ways to make computers that aren't digital. Think mechanical like the ancient Greeks experimented with, basic analogue ones that we simply started out with, quantum computing and you can even go biological.
A computer at it's essence is a calculating machine that can run several predefined programs:
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of operations, called programs.
This can be build with all four of the above mentioned types. Now a great advantage so far of digital computers is that they're both small and fast. This allows for mobile technology like a smartphone, smartwatch, gameboy and a self driving vehicle.
If computers remain large and cumbersome it's unlikely they get widely adopted by the masses. But they can still dominate large institutions and companies. I suggest you look up futurism from the 60's and 70's. They largely predicted a future without portable computers. They did however focus extensively on robotics. But if you ignore that you get a decent idea of an advanced civilization without widespread computers, at least very different from our own.
For example here we get the idea of video calling without wireless technology. This entire setup can easily be analogue.
By not going digital you run into two possible downsides. Either your machines are slow or they're large. This limits their utility. Perhaps super computers in that scenario require huge structures to support them, not a basement but an entire skyscraper. With slower calculations space flight will be a dangerous and slow affair.
Quantum computing and biological computers have no known constrains like that but getting their without digital computers might be hard. Biological can grow from a society that perhaps focuses on bio-engineering. Cloning brain like structures or even using human brains.
A bio tech focused civilization could be interesting. Domesticated bio engineered slaves perhaps, bred for different tasks. They might not share our system of ethics. Science that relies on number crunching might be a slow endeavor without digital computers but it can be done. We put people on the moon without it.