Difference between momentum & KE. Please, help.

two days of searching and reading and still i can not comprehend these concepts.


what i know:
1)momentum is vector and energy is scalar. Well it gives no intuition to me.
2)i know that Force x dTime is change of momentum. This really make sence.
3)i know that Force x dDistance = KE This makes sence too.
4)i know that momentum and kinetic enegry are like space and time.. One acts in Time the other acts in space.
5)i know two objects can have same momentum and different KE. This does not help my intuition...

I can't even formulate the question... I mean .... eh.... well that is THE difference on the INTUITION level?
Maybe my question is wrong by its own nature? Maybe i need not Differentiate them but to UNITE?
If so... how to get intuition about their influencing each other (how KE "flows" into MV and vice-versa)?

subquestion:
if i apply force=1N for 1min of time to some Object
AND OBJECT does not move AT ALL (i.e. friction is to strong)

then i have
I=F(t1-t2)>0.

BUT this equation
F(t1-t2)=m(v1-v2)
can not hold, because (v1-v0)=0 AND F(t1-t2) >0
There is a mistake in my resoning! I can't find it. Help!!!