Hi Jacob,
I'd say you got a pretty good price for the four of them! I've only ever used a DC01 and DC03 briefly; they do have weaker suction power than later models DC04 onwards (though only noticeable when using the tools) but are nice cleaners still. Good to see that they still have the attachments onboard, so many people lose them over the years.
You'll have to examine the DC05 when it arrives to troubleshoot why it won't work, but you've listed the main reasons- other possibility is a faulty switch. They are quite easy to disassemble and work on following various guides online. I'd usually start by unwinding the cable and see if it is visibly damaged, badly twisted etc- try cutting off around 15cm of cable at the end and attach a new plug if it looks worn. Sometimes it is the simplest things! A continuity tester (cheap one is fine) is very helpful in working out where any loose connections etc are.
Let us know how you get on.
Rob