It looks like your coin door is missing the lock out coil which isn't needed in the home environment. I'd just tape up those cut wires because they do have some voltage going to them and you don't want them touching the metal and grounding out. If any of those cut wires have the same jacket cover they MAY (read: MAY) need to be connected to complete a circuit. If that's the case, I'd just trace the wire to see what it eventually connects to and if it's important to operation, then resolder it. I'm assuming you've checked all your fuses for correct values and if they're not blown? Regarding the burnt coils, one thing I (and many others) do is wait to get the replacements and desolder one wire at a time while removing the old and attaching the new one. Now you took photos so you can refer to them for the correct connections. Yea, like stashyboy said, the coils probably fried due to a misadjusted switch. A sling switch was probably stuck closed and the score reel probably couldn't find home due to a misadjusted switch on its assembly and kept running and running. They're always other possibilities but these are the most common. Like I said earlier, I'd forget about playing it till you've gone through all the switches in the machine. Clean and adjust as necessary. If you don't have one already get a switch adjustment tool. Regarding switches though, like Clay's said before, if you have to adjust more than like 1% of them, you're probably doing something wrong. Unless, someone else had their fat fingers and screwdriver in there a lot. One great source besides pinrepair.com is Clay's video site pinballninja.com. He has over eight hundred repairs on there and several hundred have videos attached to them. Some people learn better with video. To join it you have to donate about twenty or twenty five bucks (one time donation) via paypal to Clay and he'll give you a username and password. You can find more info on his pinrepair website. I'm cheap but it's totally worth the cost.
Oh, and get some green Heavy Duty Scotch Brite pads at Home Depot or Lowes and clean them jones plugs. Though I really don't like recommending these guys (Ray's ok) , this EM repair video has some good info.