My freezer started warming up last night and today I removed everything and the cooling coils in the back were packed in frost and ice. I defrosted it and tested the heating element with an ohm meter and there is no continuity between its connectors. I ordered a new heating element today and left the old heating element out. I put the refrigerator ack together and plugged it in. It started working, but after several hours the fan in the freezer wuite running and I don't hear the fan at the back (on the condenser) either. The freezer is only about 24-25 degrees, so everything is defrosted inside now.
Will the freezer not function properly with the heating element out of it?

Yes it will work until the coils frost/ice over again.

Sounds like the unit may have gone into a defrost cycle and that is why the fans shut down, it should come on again in half an hour or so.

I had to go out last evening for several hours and I unplugged the refrigerator before leaving. When I came back home, I plugged it in and it still made no sounds and no fans started running. I went a took a shower and upon returning, the rear condenser fan had started. Te interior fan started about 5 minutes later or so and now (12 hours later) the freezer is down to 0 F and things seem to be working. I have anew defrost heating element on order, so hopefully after installing that, everything will be working perfectly.
THanks for you help.