You probably just need the system enabler (System Enabler 040) for the Q610 installed in the System folder. It sounds to me like someone has popped a drive from another model into this one, and under System 7.1, this can lead to just the problem you are having. 7.1 requires specific resources for each machine it is installed on; from 7.5 on, this inconvenience was left behind.
Without a floppy boot disk, however, you aren't going to resolve this problem (Catch 22), so the best thing might well be to download the free 7.5 from Apple and go from there. 7.1 on any Centris/Quadra is very fast and lean; 7.5.5 is much more bloated (and complete), but the 610 will run it just fine. Mind you, and as you have discovered, you might need to do some Googling on what to do with the disk images you get from Apple if you are going to do the downloading, etc. on a pc. Not having done it, I cannot advise, but I gather that it can be done: http://macfaq.org/index.shtml item 6.