Hello,
You have probably tried cleaning the LC II logic board already (there have been reports about people using a dishwasher with pure water for cleaning a bare board).
Yes, using the G3 would not be a bad idea. If necessary, with access to a suitable Mac(DB-15)-to-VGA adapter, it may be possible to use a PC monitor.
Once the beige G3 desktop is working, there are several data transfer methods available:
1.44 MB floppy disks written on the G3 can be read on many modern computers via a USB floppy drive (special software for Mac disks required on a Windows PC).
A SCSI Zip drive can be connected to the SCSI port of the G3. The Zip disk can then be read through a USB Zip drive on another computer.
The G3 has built-in Ethernet, and can be connected to a router/switch. Transfers can be carried out through a local network or over the Internet. FTP software may be used, or one can send files as email attachments.
A null-modem connection between serial ports (using standard terminal emulation software with file transfer capabilities) is yet another alternative.
Do not expect the staff in any computer store to be familiar with old machines.
Jan