Mymachine was out in garage and pipes froze is it safe to now turn it on

the pipe froze into the 'sore'?? Soil?

Do you have a hairdryer? Gently using hot air will defrost anything.

try a little force it should turn try till moves, left out right in

the cold water valve is at the end of the hose at the back of the machine
if the cold water pipes run outside to the garage , it is a fair bet that the water in the pipes has frozen
easy to check --take the cold water hose of the tap and see if it runs
if it runs replace the solenoid for the cold water valve

Cut pipe in half at leak and put a rubber repair coupling on.

Insulation only slows down the transfer of heat (cold), it does not stop it. If it is below freezing and the water in any pipe is not moving, it will eventually freeze. Most major industrial supply houses like McMaster-Carr or Grainger in the US, carry pipe tracing tape. It comes in various lengths and you secure it to the pipe under the insulation, plug it in and many types have integral thermostats that keep the pipe above freezing. If you have a washing machine, you will have to consider the lines to the washer valves, both hot & cold and any other areas in the washer that may hold water like the pump and the discharge hoses.
Was this washer always outdoors?

make sure it has 24 cubic feet of combustion air around it and use type b double wall for the collar diameter and pipe to factory specifications and local codes, flue must always be sloping up.

Yes, if you had any sort of blockage that kept the water from flowing out, it would accumulate in the drain pipe and once freezing temps showed up, it most likely froze. You might try putting as much HOT water down the drain as you can to defrost the pipe and then try you plunger or auger.

A professional drain cleaning company could probably solve the problem much quicker if time is an issue for you.

water freezes. sounds like first your fill pipes were froze then the pump froze. if you can find a place inside the house for washer or you may have to build a room around washer and dryer and heat it

generally speaking a sealed combustion system is inherently more safe than a system that draws it's combustion air from it's ambient location. however, it cannot be considered 100% safe in a potentially hazardous location. The actual system that would be used in a "code compliant" installation would be a 100% outside air unit.
That being said, you can install this in a garage, the vent that you are referring to (if it is a standard mobile home system) is generally directly above the unit and usually no longer than about five feet. It also requires a listed and labeled termination "cap" If you install 90 degree angles or extend the vent too far you will have issues with condensation in the piping that will cause the pipe/ heat exchanger to fail prematurely.
If the system is a 90+ efficeint unit then the PVC venting is generally allowed to be about 30 feet long, with a 1/4 inch per foot pitch back to the unit for condensation, also the general mfg. instructions allow either 2- 90 degree or 4 45 degree fittings in the line. hope this helps

turn off defrost unit likely dirty clean evaporator and condenser normal operation pipe that is froze should be cold and sweating. little pipe should be warm good luck. Tom