Interesting, not sure what's going on with the cartridges not loading. To be honest, I've never put a physical cartridge in mine (Dad didn't buy any when we bought the system in '84 (side-note, that made this computer mine and mine alone, since my siblings couldn't be bothered to hand-type any programs :D ), and I haven't bought any since pulling it out of storage). But from what I know of the VIC-20's memory map and startup routines, that should be all you have to do.
The cart has a ROM chip in it, which hooks up to BLK5 ($A000) in the VIC's memory map. The KERNAL ROM chip (marked 901486-06 on top) looks at $A000 to see if there's bootable code there. If so, it loads whatever is there. If not, it passes control over to the BASIC ROM chip (marked 901486-01). Maybe something wrong with the cartridge slot, or the cartridges themselves?
As for ROM and disk images, Zimmers.net has what you need:
http://www.zimmers.net/anonftp/pub/cbm/vic20/index.html
I mentioned the XE1541 cable and 64HDD, so here's more info about those:
XE1541 cable you can
build or
buy (there are other places to buy the cable, too)
64HDD software
The basic idea is you load the 64HDD program onto another machine running DOS (I use FreeDOS) that has a parallel port. Hook the XE1541 up to the computer, then up to the same port you connect a disk drive to on the VIC-20. You can then load ROM and disk images by using the standard LOAD"PROGRAM",8,1 commands. Let me know if you need help on that.
Before you do that, of course, you need to expand your VIC. In unexpanded form, you can still load some ROM and disk images, of course, but a limited set. Generally speaking, anything that came on a cartridge wouldn't be able to load, as you don't have enough free RAM. There are quite a few ways to do this (from buying a RAM expander cart either new or original, or building your own). I went the "build your own" route, and followed these instructions for an "internal" expansion:
ftp://www.zimmers.net/pub/cbm/documents/projects/memory/vic20/32kB.html
Basically you assemble and wire the parts on a board, then solder wires from the board to the cartridge port (on the underside of the mainboard). Works perfectly.
Other links I've found useful:
VIC-20 FAQ
Information on the VIC-20 ports
Manuals for various things
The CBM section from Zimmers.net ftp, which has links out to plenty of other things
A whole bunch of books that have been scanned
The
C64 wiki has a lot of info that's applicable to the VIC-20,
such as this screen about how to use the LOAD command
I probably have a couple dozen other links around here, but that should be enough to overwhelm you. :D