Now you've got him and I'm assuming you're expecting a bit more of him than to just plod around lazily, so he's gone 'Well bugger this, it's too hard, I'm going to be stubborn about it'. I had a mare who did that to me, she was 10 years old and the owner had only ever trail ridden her on a long rein at walk and trot. She wanted to start doing a bit of dressage and pony club on her, so leased her to me for 12 months to get her going. Well mare was NOT impressed when she was being made to get off my leg and actually travel forward. She wouldn't stop like your's and refuse to move, instead she would run flat out sideways into my leg and crush it against the arena rails. You could stick a spur in her guts, belt her with a dressage whip and she would continue to do it.
Once they work out that you're not giving up, and life is actually easier when they go forward, they're not a problem ;)
Maybe try riding like a beginner. Bit of a different method I know, but some horses will respond to that. So throw your reins away, and get him out on a trail and let him plod along. Then put your leg on a little and see if he'll go forward. Just casually, I bet he'll be happy to be out on a trail and forget that he's meant to be refusing to go forward. Train him to get off your leg out of the arena so he's got space and doesn't feel confined. Plod him along, ask him to trot, then back to walk, then trot again. Make it fun and casual, don't ask for any more than for him to react to your leg.
When he's happily moving forward on a trail, bring it back to the arena and see if there's any difference.