Can F1 use EAD to do intern?

I am a F1 since 2003. I got a EAD in 2004 because my hu*****and's I-140 was approved and we submitted I-485. But I always kept my F1 status and recently just extended my I-20 for the summer.

Right now, I got a intern position. I applied CPT but it is denied. Can I use my EAD for the intern? Will the school be angry at me and sue me illeagle? My hu*****and is a H1 in the school. Will he be sued? I really need your help. Thanks in advance.