Power a laptop LED backlight with NiMH batteries
We don't know what's in the LED backlight circuit, so your question can't be answered.  For example, if there is a switching power supply in there that regulates LED current, then a higher input voltage would probably be OK.  However, if it's just LED strings with a resistor in series with each, then the higher voltage will cause excessive LED current, which would significantly shorten their lives.

One way to tell is to vary the voltage from 24 to 27 V and see whether the display brightness changes.  If it does, assume the LED and resistor topology and don't give it 30 V.  If the brightness stays reasonably constant, then something is regulating the LED current, and up to 30 V is probably OK.

Another thing to look at is the current drawn as you perform the test above.  If the current goes up with voltage, then assume the LED and resistor case.  If the current actually goes down with increasing voltage, then you have a switching power supply in there.  If the current stays relatively constant, then there is a linear regulator in there.  You can probably get away with 30 V in the second and third cases, although be careful about the linear regulator overheating.

One problem is that 30 V is a common maximum rating for transistors.  In a high volume product intended to work with a bit less than 30 V, quite possibly some of the components are only rated for 30 V.  No matter how the tests above work out, you should be careful to not exceed 30 V.

The safest thing to do is to put the batteries in parallel instead of series, then make a boost converter to produce a regulated output voltage in the range that you know the backlight is intended to handle.