I blew an deflated balloon laid/laying on the street
I think it'd be "lying", if you just came across a balloon in the street and didn't know how it got there. It could also be "the balloon someone laid in the street", if you watched somebody put it there. But I'd go with "lying".
The rest of your sentence doesn't make any sense. Did you blow up the balloon? If so, it wasn't just lying in the street anymore. Did you blow it away? Also, you'd need to use the article a instead of an, because the next word starts with a consonant.
Try: "I blew up the deflated balloon I found lying in the street."