First... thanks for your patience! It's not often that I can't squeeze a customer in even when busy at work, but today was an exception.
With the EGR eliminated, I'm still not quite sure which direction we'll be headed. If the CHECK ENGINE lamp comes on again, by all means have the engine scanned if possible to see what it's trying to tell us. The 98 models don't support a customer code-read feature of any sort, so you'd have to actually make a date with a scan tool somewhere. Autozone parts stores and AAMCO transmission advertise free engine scans if that would help.
But EGR was only a small part of the picture, something that will crud your idle up but not prevent the engine from starting... especially if you use throttle. I'm still trying to imagine what this dead-end vacuum hose would have to do with idle quality if it didn't somehow also involve the EGR system. Here's a (really simplified) diagram of the vacuum hose routing of the 98 Stratus 2.4 engine...
If you could backtrack on the hose in question to find its source, it might shed some light on the subject. Let me know if it's one of the tiny hoses or something a bit more substantial.
How has the car been running since the time you first wrote, Joe? Is it still rough at idle? How's performance above an idle now?
Any more stalling? That would probably set the CHECK ENGINE lamp again if it did, so be sure to do what you can to obtain codes if at all possible.
Did this start soon after a refueling stop by chance? If so, there may have been water in the fuel, which will tend to dissipate over time as it's ingested by the engine. Thisis a wet time of year in many places, which makes me wonder a bit. Let me know.
One more question. Was the car running 100% OK before the stalling event... then the rough idle problem? Were there times when it might have had any of these problems before, if separately?