If never cleaned before is it a good start. Do change the paste for the cooler as well,enough tutorials online for doing that.Maybe heat is why it is shutting down that fast.
Might also want to reseat parts like ram and gpu when cleaning the pc, well if having a dedicated gpu.
If you have a compressor is that preferred yes.If a powerfull one make sure it's not blowing to hard.Can also use a paintbrush for cleaning.
Make sure to look under the fan of the cpu cooler as well,might be a "blanket" of dust there too.
And of course make sure it's of the power before starting.