Let me try to summarize:
- You were asked to do something that was impossible for you to do.
- You told your boss that.
- Boss suggests asking someone else to help
- No one else would help.
- Boss gets upset at you because the job didn't get done.
I'm not really sure what there is to do here. The only legitimate complaint your boss has is that you could have skipped step 2. You could have gone directly to someone else and ask for help. I don't think that would have changed the outcome, but at least it shows that you tried to resolve the issue on your own.
The rest of this mess is on your boss. He could have purchased the equipment himself. He could have given someone else the authority to purchase it on your behalf. He could have assigned this task to anyone except the lowest ranking person in the office. And he could have not complained about you to everyone.
If this ever happens again, ask your boss to give you the authority you need to get the job done. When you realize you do not have the means to buy the equipment, you should ask your boss to email someone else who does. Without that explicit grant of authority from your boss, I don't see how anyone else would help you. Your boss should say to that third person, spunkpike will handle everything, we just need you to provide your credit card. This is something your boss should have thought of on his own, but he didn't. So you have to.
Congratulations, you are the scapegoat! I wouldn't try to repair your image. There's nothing really to repair. You can expect that most everyone above you already knows you got scapegoated. Going forward, just be good at what you do and no one will remember this whole affair. The positive outcome from all of this is that no one will ever ask you to purchase stuff again!