I thought the glycerin was a prerequisite for making any kind of soap.
At it's simplest, soap can be made with a fat and caustic. Glycerin is a fat and will work, but you can also use lard, beef tallow, coconut oil, olive oil, cocoa butter - or the baked on greasy crap in your oven or on your stove top. Try using a little KOH solution on a rag for starters. You may find you need a thickener to get it to stick to vertical surfaces and soak in, but it should at least start to loosen and maybe remove the built up crud if you add a little pressure while wiping it.
Will do.