Your screen on your Gateway SA1 went black at startup and a fan is running but no drive indication light is on. What can a probem be you ask? You unplugged a power cord and took out a battery, held a power button down for sixty seconds, then replaced power cable and that computer still will not boot.
You can try booting that laptop without a battery. Also, please unplug or take out any unnecessary devices ie. USB memory stick, DVD, etc. You can try hooking up an external monitor to that laptop and power it on to see if it is that screen that went bad.
Try taking a hard drive out and then reseating it. You can try blowing out any dust with canned air or air compressor out of a system fan. Another thing you can try is taking out memory and reseating it.
If there is more than one memory stick, you can try booting it up with one stick at a time to eliminate potential of a bad memory stick. This Gateway additional SA1 memory page shows what screw and cover to remove to get to memory. You can reboot it and power it off a couple times to make sure it is fixed.
Test each stick of ram one at a time. Also, it sounds like you have two DIMM slots or memory slots. Test each memory slot at a time.
If both memory sticks work in slot A or DIMM 1 for example, then it's not bad memory and is a faulty memory slot. If only one stick works in slot A or DIMM 1, then one of those memory sticks is bad. You want to isolate whether or not you have a bad memory stick or bad memory slot.
If you have a bad memory stick, then you will want to buy same kind of memory replacement. If it is a bad memory slot, then you will only be able to use one memory slot. What you could do is buy another single piece of RAM memory that is larger ie. 2 gig instead of 512MB.