I'm not sold on ripping up the carpet. Your sump pump SHOULD (if built correctly) have SURPRISINGLY clean water that was discharged out of it. Like this time of year, that's snow melt, etc. So it's already clean ground water, and then further filtered through drain tile/rock fill.... I would drink that straight up over Flint water any day.
Seriously, fix the PVC (easy) and repair it. Curious how that happened to begin with. Ensure that the discharge line is using properly pressure-rated schedule pipe and that all joints are sealed properly with the CORRECT primer/glue.
Next, get a dehumidifier and run it to the now-fixed drain so you're not emptying the bucket 1000 times.
Get a water extractor from a rental place. Your carpet and pad will be fine.
Mostly importantly, they sell alarms with a water sensor attached. Buy them!!