Turns out you will not need either one of the adapters we suggested. What you need is the Cable, HDI45 to DB15, Display Adapter. Visit this site to take a look at it:
http://support.apple.com/kb/TA23337
The 15" MS monitor will plug right into the LC 475. The 6100/7100/8100 series of computers adopted a different high density monitor connection. If you look at the top adapter, Cable, Adapter, 45-Pin, you will see all the components that were built into the HDI45 plug. That octapus cable is the opposite of what you need for your multi-sync monitor. Fortunately, that style of HDI died in one generation.
You said that the monitor on the LC475 is dead. Maybe not. First, look here to make sure we are talking about the same computer:
http://www.everymac.com/systems/apple/mac_lc/stats/mac_lc_475.html
Try this trick. Turn the computer on at the power switch. Leave it on for ten seconds to load the capacitors and all, then turn the switch off and back on quickly. That might wake up the video circuit to the monitor. Details on why later if you want to know. A dead PRAM battery in a 610 or a 6100 will definately cause the monitor to not wake up. But, rather than buy a new battery for a computer you never intend to use on a daily basis, use the on-off-on trick and save the five bucks for something else.
Yes you can network the computers if you want to go to that trouble. Doing it 'headless' would not be easy. You have to configure the network from both ends. If the non-fruit colored iMac is new enough then you will not need a crossover cable. It will auto detect. If it is too new, you will have appletalk issues to deal with.
If you are near a large city with a Mac user group, you might just borrow a SCSI zip drive and a USB zip drive. A platinum G3 would also be nice. You can find them for $5 at recyclers. The original G3s will take both SCSI drives and IDE drives in the same case.
Options abound. If you are going to buy an ethernet cable, it means you do not have one. Explore other options while you are at it. If you are in the NW, we can give the name and street address of where to buy cables for $1, zip drives for $2 and G3s for $5. Good luck.
Jim~