I see the same with a friends pool when the filter gets clogged but in your case the 13 psi sounds low for a clogged filter. The pump should be able to deliver more than that. At least 20 psi unless you have trapped air in the pump chamber. A centrifugal pumps blocked pressure can vary greatly. A danger in running totally blocked is heating the water in the pump chamber to the point where the basket and/or plumbing starts to soften and deform. Even a very low flow will prevent this however. The issue with not starting sounds like a crummy starter switch. Happens frequently especially after sitting out all winter. If you need more info on this there are several threads dealing with this issue. Simple fix. If you can't find the info I'll dig it up and post.
Al