Yes, that’s completely inadequate insulation. Call a local Energy Rater yo assess the overall air tightness and insulation level in the home. Air sealing is just as important as insulation.

Also contact your local electric utility for information about any rebates or assistance programs that are available for tetrofitting the home. They often have programs in place, and an approved list of contractors.

Be sure to do your due diligence on any contractor that you hire. You want only licensed and insured people working on your home, Mr. Roof Guy doesn’t sound like the pick of the litter to me.

You need to replace all the insulation in the attic. The old insulation needs to be removed. You should also remove the floor boards that are on top of joists so insulation can be added. You can put them back when the insulation is in place.

You can hire an insulation company to do the work. Insulation choices are blown in, fiberglass batts, or spray foam. You could install the fiberglass batts yourself. I recommend R-38 kraft faced batts and seal penetrations first before installing the insulation.

If spray foam if applied correctly it will seal and insulate. You need to hire a professional to do it and it is a lot more money. The blown in type can be done by yourself with rent equipment or by a professional. In either case a moisture barrier needs to go down first. All the moisture in your house is going into the attic and condensing in the winter. A moisture barrier will help reduce this.

This other problem I think you have is lack of ventilation. Did the roofer install a ridge vent when the roof was replaced? I see a small gable vent. Is there another at the other end? It looks too small. Are there any soffitt vents? You need adequate ventilation otherwise you will continue to have moisture problems in the winter.

Sad that the inspector did not catch the water damage evidence if you had it inspected. I will largely reinforce what others have already stated. Hire an energy rater to guide you towards the right fix for the problems and the low hanging fruit for saving utility cost. Check to see if there are state or local programs that will pay all or part of it. Raters can be found at BPI or RESNET.

There are two sides to the attic moisture problem, moisture in from the living space and moisture out via venting. Venting needs to be improved. If there are soffit vents, judging from the pics, they are blocked by insulation. Moisture in comes form air leaks and compromised or inadequate moisture barrier. If you are going to stick with glass bats or go with loose fill, you need to air seal because it does not stope air flow. Don't forget the attic stair opening. That can be sealed up inexpensively with a box that you set above the opening or you can buy a zipper bag.

So much good information, thank you!

Agree with everyone here. Look for a great insulation company, get old insulation removed, add baffles at the soffits/ eaves before new insulation (insulation company has these), install soffit vents (a local handy man can add round vents) if no venting exists. The energy auditor should be able to calculate the required ventilation needed for the size of your attic.