If your display screen on your Gateway SA1 laptop computer system went black at startup and the case fan is running but no drive indication light is on, then what can that problem be caused by you ask? You went ahead and disconnected that power cord and took out the laptop computer system battery, held the power button down for sixty seconds, then replaced the power cable, and that computer still will not boot properly.
You can try booting that Dell laptop computer system without the battery installed. Also, please disconnect or take out any devices that are not necessary, for example universal serial bus memory device, digital video disc, etcetera. You can try hooking up an external video monitor to that laptop computer and then power it on to see if it is actually that laptop's display screen that is failing.
You can attempt to take out the actual laptop hard drive out and then installing it again. You can try blowing out any dust with canned air or an air compressor out of the computer system fan. Another thing you can try is taking out random access memory module(s) and installing them again.
If there is more than one random access memory module, you can try booting that Dell laptop computer with just one memory module at a time in order to eliminate the potential of a faulty random access memory moudle. This Gateway additional SA1 memory web page shows what screw and cover to remove in order to access the random access memory module(s). You can then power on and power off that laptop computer system, a couple times in order to make certain that it is indeed fixed.
You will want to perform testing on each random access memory module one at a time. Also, it sounds like you have two dual inline memory module slots or memory slots. You will want to test each physical memory slot one at a time.
If both random access memory modules work in slot A or dual inline memory module one slot for example, then it is not faulty random access memory and is indeed a physical faulty memory slot. If only one random access memory module works in slot A or dual inline memory module one slot, then one of those random access memory modules is bad. You will want to isolate whether or not you have a faulty random access memory module or faulty physical random access memory slot.
If you have a faulty random access memory module, then you will want to purchase the same kind of random access memory module(s) replacement. If it is indeed a faulty physical random access memory module slot, then you will only be able to occupy one memory slot. What you could do is purchase another single piece of random access memory module that is larger for example, a two gigabyte random access memory module instead of a five hundred twelve megabyte random access memory module.