There is a way to power it on, but that won't determine whether or not it is good. If it is really a 350W PSU with a liar-label on it, it would turn on just fine with an insignificant load on it. Under load, it probably just power off. Of course, if it won't turn on at all, it is bad. Plug a few fans into it (so it has a load), then short the green wire to one of the black ones in the 20+4 pin motherboard connector (a paperclip can be used). Google will lead you to images and/or videos of how this is done.