I agree with Rudey. Start by making it a 2 man chapter, and progress from there. Try getting your JA's in on the action ASAP. Right now they are still riding the wave of motivation and excitement of joining Delta Sig. They will be more eager and willing to volunteer or agree to do things than the already apathetic ones.
Contacting your alumni was a great idea. Many times alumni are more than happy to assist the chapter in activities. Perhaps if some people in positions aren't doing anything at all, an alumni who previously held the position could help out and guide the present position chair.
Congrats on being so proactive and taking the initiative to begin a major (and beneficial) change!