Well, cardboard was what they used most of the time. Only some of the early C64-C which still has the 'big' C64 board had a metal shielding, afaik.
Later on the new, small board with 8580 SID insted of 6581 was used. There are 2 different small board versions, and the GS board is basically the 2nd version, but has a different Rom and a 90 degree turned expansion connector as well as some other connectors are missing ( e.g. serial connector ). But the board in the GS is a fully working C64 board ! If you solder in some connectors, replace the Rom and attach a keyboard to it then you have a C64
The GS board even still has the basic Rom inside !
About your black screen C64:
That could be pretty much everything being the culprit
For a first check you can remove the SID ( 6581 ), attach a diskdrive and try typing blind diskcommands, and feel if any chips get especially extremely hot ?
On revision 250407 boards the chip failing most of the time is the PLA ( MOS 906114 ). It normally produces a black screen, but can also produce a screen in one colour or also some multicolour horizontal stripes. You can check if one of these symptoms appear if you turn it on lots of times ( 30 times or more ).