I don't know much about an IntelliChem, excect that I wouldn't want one (no offense). The IntelliChlor system consists of the salt cell and a power supply. That power supply might be mounted near your equipment pad somewhere (it's a tan box a little smaller than a toaster). The salt cell would be plugged into it. Or its power supply might be mounted inside a Pentair automation controller (do you have one?). Either way, it's a stand alone system that can be controlled either by an IntelliChem, a Pentair automation controller, a combination of the two, or on its own. So the short answer is, yes, you can run your SWG without the IntelliChem. Basically, you would disconnect the IntellliChem from your system, and as long as the IntelliChlor is still wired properly, it'll run just fine on its own. You'd control its chlorine output using the buttons on the cell. You'd then test and monitor your FC (chlorine level) regularly, and adjust the IntelliChlor's output setting to maintain the desired FC level in your pool.
If you have an acid dosing tank and pump as well, then that's a different issue and that may or may not run on its own, depending on what it is.
TFP supports manually adjusting pool chemicals based on test results from a reliable test kit. We dabble a bit into supporting some automated chemical dosing systems (like SWGs and liquid chlorine and acid dispensing systems), but we don't really get much into the IntelliChem. Based on what I've read about it, I don't see how running an IntelliChem offers significant advantages, not when you consider how you have to fool with it and keep it properly calibrated. Personally, I wouldn't trust one 100%, which means I'd want to test the water myself, maybe once a week, to make sure the IntelliChem is functioning properly. And if I have to test the water manually once a week, and make adjustments, well, that's what I do without an IntelliChem! Which is what I meant by claiming that I wouldn't want one, because it wouldn't save me any trouble, and it's just one more thing to break down.
If you want to get your IntelliChem running again, you might try Pentair Tech Support. They're pretty good. If you want to move away from IntelliChem, then we can help you do that.