A good soil test from somewhere compitent like loganlabs.com will help you immensly in determinating what needs done.
What type of grass do you have and what kind do you intend to seed?
How did you determine that your ph is nuetral? What is the numeric value?
Adding good compost will almost never be detrimental.
Seeding is best done in the fall. Seeding during the spring brings in weed preasure, Washout from spring rains, and turf survival issues during summer heat because the turf has no root system. These issues can be mitigated, but at rather substantial cost.
If you're seeding, you'll want to use a starter fertilizer and depending on what a soil test indicates, you may want to use one anyway.

What is your watering routine? How often and how long?
Are you sure the dead vegetation is dead and not dormant?

The best way to rehab your soil is to get full control of watering and to use organic fertilizer. The reason soil goes bad is the microbes in the soil are not getting fed. Organic fertilizer feeds them. Compost does not feed them. It is not detrimental, but it is nowhere near as good for the microbes as organic fertilizer.

As grass said, seeding is best done in the fall. I'd like to turn that thought around - seeding in the spring is a horrible idea. Spring seeded lawns are almost universally disappointing for the owner. The newly seeded turf grass does not have strong enough roots to make it through the summer heat, but the crabgrass seed that came up at the same time as your turf grass is evolved to survive the heat.