Suddenly, sleep command leads to window's shutdown?

When awakening the shut down computer, I get a Windows Error Recovery screen.

To me this doesn't sound like it is shutting down, it sounds like a problem sleeping or waking up.
Do you have hibernate enabled and can you test that to see if it hibernates and resumes ok?

Here is a tutorial that may help.
Gathering a Startup, Shutdown, Sleep, Hibernate, or Reboot Trace

I'm quite certain that the computer is shut down as it "on" light goes out and there certainly isn't any drive noise to be heard.

Sleep definitely shuts the computer down. No matter what I do in Power Options, when selecting Sleep, computer is definitely off. How can I be so sure?

Well, in the past when Sleep was working, there would always be a blinking blue light emanating from the computer's on/off button and when bring back from Sleep all I would have to do is tap any key or left click my mouse and without any hassle, open programs would come back. However, now when selecting Sleep, no blinking blue light, no awakening when tapping keys or left clicking mouse. To open computer I have to depress the on/off button and when the computer comes to life there is that Windows Error Recovery screen and when Firefox is opened, I'm told that it crashed and if I wanted to restore stuff.

The results of a Hibernate shut down are quite different and look to be normal. No blinking on/off light, but have to depress this button to get things started. Screen says Resuming Windows instead of Starting Windows as it did when using Sleep, there is no Windows Error screen, and I'm not asked to my user password. Also, Firefox opens without any "crash" alert.

I guess I can live with using Hibernate, but it is a real PITA compared to Sleep and I would much prefer to get to the bottom of this so that I can use Sleep.

Does Shutdown work ok?

In Power Options enable Hybrid Sleep.
Click on Sleep.
When you restart the PC does it resume from Hibernate?

The blinking light means your PC uses S1 sleep.

It may be there is not enough power to support S1 Sleep.
Maybe the PSU is starting to go, or an issue with MB voltage control.

If your PC supports S3 Sleep, you could try that.
You would have to go into bios and look for the sleep setting.
S3 uses less power than S1.
S3 will turn off all fans, the light, HD, etc.
Only power it uses is a small amount for the RAM.

You could also try using the tutorial i put in my first post to gather Trace info.
I've never needed to do that, so I'm not sure what info is in the trace.
But, it's free and may help identify the problem.

"In Power Options enable Hybrid Sleep.
Click on Sleep.
When you restart the PC does it resume from Hibernate?"
Fourth paragraph in my post above describes what happens when I select Sleep and Hybrid sleep is enabled. Apparently, and as best I can tell, the start up is resumed from Hibernate.

"It may be there is not enough power to support S1 Sleep.
Maybe the PSU is starting to go, or an issue with MB voltage control."
The computer is fairly new, about 4 years old, but it is quite possible that there may be power issues, of which I know nothing about. Logically, but naively, if the computer's Sleep was working and as you say it needs more power than S2 or S3, this could point to a power problem. So, if you know, how can I check to see if S2 and S3 are available in BIOS (don't know anything about getting to BIOS or how to find S. Also, I would like to check PSU and MB, but don't have a clue how to.

oing the Trace looks cool, but when I looked at the tutorial

If i understand correctly Hybrid Sleep works for you.
If you click sleep, then turn on the PC, you do not get any errors.
Your Windows session is "intact", the same as it was when you clicked sleep.
If that is correct, it means your PC is not doing a Shutdown when you click Sleep.

Usually if you keep clicking the Delete key when the PC is booting up you should get a screen where you can enter BIOS.
You will have to get into BIOS and look for a setting to see if you can select S3 sleep.
I couldn't find any info about this for your PC.
If someone here reads this and is familiar with Gateway maybe they can give more specific info.
I build my own PC's...

I'm guessing a power issue because:
Hibernate works, so Windows is able to save the session to HD.
Sleep does not work, and Windows should save the session to RAM.
Sleep requires power to work correctly, Hibernate does not require any power.

Hybrid sleep saves the session to RAM and HD.
With Hybrid, if Sleep fails to wake-up, hibernate kicks in and should resume Windows.

To check your PSU and MB you would probably need to take it to a shop where they can test it.
Or, if you have a friend that builds PC's, ask for help?

I always have spare PSU's around, so that's how I test.

"If i understand correctly Hybrid Sleep works for you.
If you click sleep, then turn on the PC, you do not get any errors.
Your Windows session is "intact", the same as it was when you clicked sleep.
If that is correct, it means your PC is not doing a Shutdown when you click Sleep."
You got it right. Power options are set so that when Sleep is selected the computer goes into Hybrid Sleep, as it should. However, when not set for Hybrid Sleep, but just Sleep, computer appears to shut down and then reboot with the Windows Error Screen and a crashed Firefox.

I'll try to get into my BIOS and see if I can find S2 and S3... and let you know what I find. BTW, I've never gone into BIOS, so assuming I find S2/3, how do I make the changes to select one of them?

In BIOS you use the keyboard to move around and select things.
Hopefully the keys will be listed on the screen - see my example.
Use Arrow keys, Page keys, Enter, ...

F10 should Save your changes, and ESC should discard changes.

The screen-print is from MY motherboard manual, showing where the "S1/S3" sleep setting is.
This is just an example for you, so you have an idea of what to expect.
I couldn't find any info about your BIOS in the Gateway manuals i looked at.