Ok, first thing's first. Keep your head up, there absolutely is an airline that will take you. Second, I will say that your 5 years of military experience is NOT nothing, and in fact I would imagine is attractive to employers.
I'm no HR expert, but your resume (the actual document) can make or break you, so make sure that it is clean, concise and overall professional looking. With a quick Google search, I found a service that specializes in resumes for veterans. Here is the link:
Visit VP Career Services to find information about writing your own resume, using a resume template or hiring a resume writer.
www.vpcareerservices.com
I might add that if you do not already have a cover letter, spending a little more to have them write one for you may be worth it.
Additionally, I highly recommend you continue to cast a wide net, and that may mean looking at part 135 operators as well. There are quite a few of them and they're always hiring.
Lastly, you might consider looking at starting out in a non dispatcher role within the airlines. Even if it means crew scheduling, aircraft routing, working the ramp; whatever. Airline ops experience regardless of position has a lot of value and just getting a foot in the door would help a ton down the road. Just something to consider.
Overall, just know that you will be alright and you will find something that's a good fit. I'm sorry you are having trouble right now, but keep the faith! If you have any more questions feel free to message me. I have a lot of experience applying to airlines and I'd be happy to help you out however I can.