Screen Share not working

I have two Mac Minis, one late model at work and an earlier model at home. Both run "headless" on their networks. Both have recently become unwilling to screen share after doing so effortlessly for the last few years, although I can see shared folders in a Finder window. Both can be accessed with Logmein, although the connection is slow as might be expected. All computers concerned (Minis and the laptops used to access them) are running Snow Leopard.

Any ideas?


John F