V + 不了
This potential complement usually describes something that you generally can't because of an external factor out of your control. 没有办法！
我的腿受伤了，所以我走不了 "I can't walk because my leg is injured"
I didn't decide to get injured (did I?)
这数学问题太难，我帮不了你 "This math problem is too difficult, I can't help you"
I'm unable to help you because I lack the necessary skills.
这是非法的，我做不了 "This is illegal, I can't do that"
I can't do that because the law forbids me to do that
V + 不动
This instead describes your own physical inability, and not an external hinderance.
When talking about physical feats though, you might think: "Wait, if I'm physically unable to do something, it's not really under my control, is it?". Well technically it is:
我累得走不动 "I'm so tired I can't walk"
In this example I can't walk because I'm too tired, but I could theoretically force myself to keep going (and collapse shortly after).
The two of us can't physically carry the shelf, but there's no external factor stopping us from doing it anyway (and get crushed afterwards...).