It would be pretty close to impossible to complete a thru hike on just $500--unless you raided the hiker boxes and became dependent upon handouts (and I don't think I could personally be proud of completing such a hike).
My biggest concern for you would be a lack of proper nutrition. Hiking burns a lot of calories (Most people need to consume over 5000 calories per day on a long hike). Lack of sufficient calories and a lack of proper nutrients can cause long term damage to bones, joints, muscles and bodily organs. Such problems CANNOT be prevented just by taking a daily multi-vitamin. You will need to actually consume enough of the (right kind) of calories. You could even face long-term problems such as diabetes and bone/joint issues due to a lack of proper nutrition on a thru hike (these problems may not surface for many years). A thru hike isn't worth a lifetime of health problems or an early death.
I recommend that you start a little later and do a SOBO hike. You will probably have better weather for most of the hike and possibly need less cold weather gear.
Work like heck until your hike starts. Work 2-3 jobs and work as many hours as you can. In addition to that, mow lawns, shovel sidewalks, sell plasma, register with temporary employment agencies, collect and sell aluminum cans. Do ANYTHING (legal) that you can possibly do in order to earn more money.
Look around your house or apartment. Sell items that you do not need (use ebay or a yard sale). Try to borrow money from friends and relatives--with an actual contract or agreement to pay it back. (Then pay them back!). Cut every non-essential expense from your daily living. Use coupons to reduce the cost of food and other items. Search the internet for sites that tell you how to cut living expenses.
Every extra $150-180 dollars that you can earn (or save) is an extra dollar per day for you to use on the trail.
If you start your thru hike 1-3 months later--and save more money prior to your departure--you will have a much better chance of having a successful thru hike and reduce your need to drop out early due to a lack of funds.
Good luck!