You're probably not formally banned, but that just means that a border guard will be _allowed to_ let you in without losing his job over it, if he believes you're really a genuine tourist or business traveler.

But they never _have to_ let anyone in. And with the background you're presenting here you will have a devil of a time convincing any border guard that _this time_ you really truly actually intend only to visit. Then you'll be sent back anyway.

Also, if your asylum application was filed _after_ your 90-day VWP status ran out, then you have overstayed on VWP and even one day of VWP overstay means that you're **forever barred from entering under the VWP again**. It would be helpful if the ESTA system detected this and rejected your application outright, but this doesn't mean that you won't be turned away when actually arriving in the US, if they discover the overstay at that point in time.

All in all, this sounds like a lost cause.