"The battery has (a) full charge."
"The battery has (a) 40% charge."
"The battery is at (a) full charge."
"The battery is at (a) 40% charge."
"The radio needs a battery with (a) full charge."
"The radio needs a battery with (a) 40% charge."
Do I need the article "a" in these sentences?
I imagine that you have had no response because some of us are not sure! I would say, "The battery is 40%/fully charged". Here is my guess at your sentences:
"The battery has a full charge."
"The battery has a 40% charge."
"The battery is at(a)full charge."
"The battery is at(a)40% charge."
(Neither of these sounds very natural to me.)
"The radio needs a battery with a full charge."
"The radio needs a battery with a 40% charge."