I understand that "equipment" is an uncountable noun.
So, it cannot be replaced with "one".
The following sentence is wrong.
Ken replaced the broken equipment with new one.
Yes, you are right on all counts. Even in contexts in which "new one" can be used, it would be "with a new one" not "with new one."
The alternatives des3 has given are OK. If you wanted to be able to use "with a new one," you would need to put "piece of" between "broken" and "equipment":
- Ken replaced the broken piece of equipment with a new one.
That means, of course, that Ken replaced the broken piece of equipment with a new piece of equipment.