Control - Open Apple - Closed Apple - Reset. Your system will flash several patterns of colored squares, after which, if everything's good, you will hear some rapid beeps, and the message "System OK" will appear on the screen, If there's a problem, you will get an error message. A ram error will be displayed with a series of 1s, and 0s equal to the number of RAM chips. The 1s will represent the problem chips. For example 01000000 would mean that the second chip in a line of eight is bad.
As for the price you were quoted, sadly that's pretty reasonable, especially if he/she is including the replacement RAM, and/or sockets. Installing the new chips is relatively straight forward, but removing the old ones cam be quite time consuming. This is at least an hour, to an hour and a half of work, maybe longer if something unexpected happens. Ultimately, your not paying for the parts, or even the supplies, it's the time that's the price killer.
If you want to do this yourself, you'll need the following, A soldering iron, some solder braid, a solder sucker (get both), some electrical flux, and of course solder (lead free will work, but leaded is easier to work with). Going with the cheapest of these that I've found, the cost will be over $50, and I know that I'm leaving some things out. Also, find something to practice on (like a dead cartridge game, or something that won't be missed). Trace separation is a real issue on these older machines, especially if you're new to this kind of soldering. Personally, I learned this the hard way. And if you're hand slips, you could end up causing even more damage (Something else I learned the hard way).
For a good tutorial on soldering in general, check out the Ben Heck Show, and The 8-Bit Guy on YouTube. There's another who's name escapes me, but he's always saying "In like Flynn" when he opens a case. He's informative, and good with a soldering iron, but the repeated reference to the guy who played Robin Hood, and his unfortunate preferences for underaged girls kinda bugs me. But if I run across one of his videos again, I'll let you know.
As to any Tutorials regarding the Apple //c itself, I haven't found any. The closest I saw was a man who "fixed" his //c by buying a new motherboard (cheater).
Edited by DistantStar001, Sun Jul 22, 2018 12:18 AM.