We're in the same situation. I can't tell you how to motivate parents. In my experience, either they feel it's important and are willing to make a huge effort, or they can't be bothered. The latter are the ones who give their kids the message that school isn't really very important.
Of course, there are parents who care and just can't find the time.

Some possibilities:
Contact local service organizations. Sometimes they give chunks of money to worthy groups.
Ask for donations from local businesses. Money, lumber, free "rental" of equipment from a rental outfit. We did a spaghetti dinner with most of the food donated. Of course, you still need volunteers to make phone calls and to do the work, but it doesn't take as many people if you have help from local businesses and service organizations. It's amazing what you can get done if you have someone willing to make those phone calls.
Check your local office of education, arts council, etc. There are many grants available for a variety of needs. It involves some paperwork, but it is often fairly easy to fill out the forms. Even if the grants are not for what you want, perhaps a grant can pay for some of your regular expenses, freeing up some money for special projects.
Good luck!

This might even be a project for a Boy Scout Eagle Award project or a Girl Scout Gold Award project (engineering/designing, fundraising, co-ordinating volunteers, and acutal construction). If the Scout council would approve the project AND if it inspired a Scout, you might have found yourself a project manager. This would probably not give you a playground this year, as this is a somewhat slow way of going. But it is amazing what an enthusiastic teen who really CAN take charge will do for parent volunteers.

One other thing is to be sure your PTO is having fun. You will get more volunteers and retain the ones you have much longer if the PTO has some fun things going on. Have the PTO have a potluck dinner after a spring cleaning Saturday, or do a PTO sponsored family dance one night.

The local county, city, and private schools in the county where I live have gotten together in their fund-raising efforts and put together a coupon book. Coupons are from stores, restaurants, Car wash places, Oil change chains, even WalMart's is in on it. The coupons usually say that you either get $2 off on a $10 purchase of children's with the stores name on the coupons of course...clothes for 20% on a sales item at the particular store, or 25% off on ladies clothing or whatever at a different store. Restaurants have coupons -some chains like McDonal's are in on this with a few coupons -some restaurants have deals like buy one breakfast of juice, eggs, bacon get a second FREE or buy one dinner get Appetizers 1/2 price, buy one dinner get second 1/2 price, buy one burger (certain kind) get second Free on and on. Many times this is a good way for stores to get business from customers that have never been to their stores or restaurant or Nail place etc. It could include several counties for that matter.
*I thought it was really good. That way all size schools benefits. The profits for selling of the coupon books go directly to the school where the coupon books are bought. The books sell for 10 dollars but has tons of coupons. They are huge sellers. Beats trying to sell overpriced chocolates and items that people just don't care to buy.

What about contacting a high school that require service hours of the students? The school I teach at has adopted a nursery school. The students go afterschool and help out with things that need doing, fund-raisers, help provide for school parties, etc. The high school kids enjoy working with younger kids & earn their service hours in a great way!

How large is the community? What about local business? What about the farm organizations? Do you have a Farm Bureau? What about insurance companies? What aboput 4H and FFA clubs? I would check with business people and count extension service. Try and get the kids to collect items by letting parents know what you need.

Yes in this county they have businesses that "Adopt a school". That means the business spends a certain amount of money helping the school get what they need. This is usually a large business that does it. But smaller businesses could do something similar.

Ever hear of a playground map? Adults and students can easily stencil and paint these huge maps. I think they are under $500

Here is a link that might be useful: playground maps