Can I use the adapter from my gaming laptop to give it power?

If its the same type of connector and the same voltage yes.

Possibly. If the output voltage, amperage, polarity and adapter tip are the same, then it shouldn't matter. Otherwise you can damage the unit if they aren't the same.

The netbook adapter according to some website
----------------------------
AC Input: 100 ~ 240V 50~ 60Hz
DC Output: 19V 1.58A 30W

My laptop adapter says
----------------------------
Input - 100-240V~1.5A 50-60Hz
Output - 19V a line with dots under it 4.74A

So that's a no then. P=VI = 19V X 4.74A = 90W. Three times the power input will surely fry your netbook. A line with three dots underneath means DC (direct current). A line with ~ underneath is alternating current.

Just look at the dc output. Obviously the ac input will be the same for all regular electronic devices since that's the voltage and frequency range for which a wall outlet will deliver.

That's just the maximum wattage the adapter can supply. It doesn't mean it's going to be "pushing" that much into the device.
The voltage must match but amps can be higher.

Yes it is going to be pushing in that much. If the netbook can still further regulate the higher input because it was rated to handle it, it's fine. If it can't provide sufficient resistance because the input was more than it was designed for, the netbook will get fried.

I don't think that's right. The netbook will only draw as much current as it needs. The laptop power supply will have no problem in that department. The voltage specs are the same. If the plug fits and has the same polarity as the original, it should work.

I don't know. The netbook needs to be able to handle the higher input properly. Think of the human body. A mild shock the body can resist but ramp that up to sticking your finger in an outlet or getting struck by lightning and your body cannot overcome the extra power since you weren't designed to handle that much.

The netbooks input specs need to be checked to see how much input it can handle.

Trust me, I'm an electrical engineer. ;)
Voltage matters.
Amperage is determined by the consumer (notebook in this case) and what is rated on the adapter is the maximum value supported by the adapter (if you supply a consumer that draws more current than that it will fry the adapter).

This.

A long time ago I accidentally set my adjustable power block to 4.5v rather than 3v for a tape player, the player was fine, but after a while a part of the case got soft, I unplugged it and the player worked fine, but I almost certainly decreased the lifespan.

Mind you a tape player, even the fancier ones with auto reverse and a radio built in are likely far more resilient with incorrect voltage than a laptop would be.

Under my netbook, it says this
------------------------------------------
DC RATING a line with 3 short lines under it 19V, 1.58A

Just plug it in and try it out.

This isn't like installing a piece of software GameRager.