If the computer will run on AC (usually through an adapter) with the battery installed it's possible it is charging but a fully discharged battery takes a very long time to come back to useful charge. If you haven't left it on for at least 24 hours it may just have not had time to come back to life. Even at 24 hours charging may not be complete if you started with a fully discharged battery, but should be up enough to tell that it's getting some charge.
If you have the common Lithium Ion or Lithium Polymer battery, the normal charging cycle is a constant charging current until the battery comes up to normal voltage, but then the charging current is reduced to 10% (or less) of the intital current value to complete charging. Full cell voltage is reached at less then 40% of full charge, so when the input current drops it takes a long time to actually "fill it up."
If, with this kind of battery, something turns on when you try to start the computer with battery-only power, but it just dies almost immediately, leaving it on the charger for longer may finish the charging. Depending on the charging system built into your computer it could take several days.
With Lithium batteries the voltage does not increase after the battery is up to the "format voltage," and the slight resistance change that happens when the battery is "full" is too small (and inconsistent) to be used to control charging. (i.e. there is NO practical way to tell when the battery is fully charged.) Overcharging will destroy the battery, so most "chargers" built into laptops use a very low "finishing current" and a timing circuit to guess when to cut off the charging, hence getting past the half-way-charged point may be a very slow process.
Your battery should be labelled to show what type it is since in most places it's a cert requirement so that proper "toxic disposal" can be done. If it does not indicate "Li" or "Lithium" then you have one of the other kinds, with different rules to be used.