Start with one problem. The purge valve. So that indicates that you either have no power or no control (ground) at the PCM. The purge valve can be annoying to troubleshoot if you don't have a scan tool with bi-directional control. It can be done, but it's going to require you to unplug the pcm and run continuity checks all the way back to the purge valve. If that's something you want to do, I'll walk you through it, if not, I'm not going to waste my time typing it all out.
The A/C circuit is the same. Much easier to troubleshoot with bi-directional control, but it can be done.