There are four things to check.
One: Processor Fan
Two: How dirty the computer is inside. (Plus PSU)
Four: Electrolytic Capacitors on the motherboard.
[Note* PSU = Power Supply Unit, or simply power supply]
One: If the Processor fan has stopped spinning, the processor will overheat. Since the Aspire M1100 series desktop computers, use an AMD processor, the processor can overheat in less than 30 seconds, without external cooling.
(Intel's take longer)
The BIOS program in a computer, is what turns the Processor on, and also what turns it off.
If BIOS senses no processor fan operating, or the temperature of the Processor has exceeded the processor's thermal limit, the processor is turned off.
Keeps the processor from burning up.
Computer case open, do not stick your hands inside, turn the computer on, observe the processor fan. See if it's rotating.
Observe for a small length of time, to see if the processor fan spins, but then stops frequently. Also the fan may be spinning at a slower RPM, than it should.
Solution is to replace the fan, but cost wise it may be more effective to replace the Heatsink, and Fan as a unit.
To replace, the computer is off, and unplugged from power.
Computer case open, TOUCH the metal frame of the case to relieve your body of Static electricity.
Your body carries Static. Static will fry out (Short Circuit) the delicate computer hardware components inside.
Simply touching the metal frame will alleviate this.
[Note* If you get up in the middle of working on your computer, upon your return Touch the metal frame again.
Or wear a $6 ESD wrist strap, and connect the alligator clip to the metal frame]
This is what an average processor Heatsink/Fan combo looks like, if you are not aware,http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=1116581&sku=TC3G-2028
If you are aware, please ignore the above, and the following.
Heatsink/Fan combos differ in their appearance, and design, but all follow the same theory.
In the photo, the Heatsink is the finned aluminum looking object under the fan.
The Heatsink is composed of a metal flat plate, that has tall fins protruding from it.
Heat from the top of the Processors case is absorbed by the metal plate, and radiated up into the fins. The fan pushes air in-between the fins, and carries the heat away.
Therefore the area in-between the fins, the fins themselves, and the fan must be kept clean.
Doesn't take very much 'gunk', (Dirt, dust, hair, etc) to drop the cooling capacity of these two components, tremendously.
This goes along with number 2 above also.
Two: The inside of the computer, as well as the inside of the power supply, must be kept clean.
Preferred method, is to use a can of compressed air on a regular basis as needed.
[Computer unplugged from power. Anti-static guidelines as detailed above, implemented]
Three: Power supplies can fail. The power supply can develop a weak voltage power rail, and not have enough power to turn the Processor on.
It will have enough power to light lights, and maybe spin fans, (Or spin a few times, and stop), but not enough for the processor.
A) ALL the lights use less than 1 Watt of power
B) EACH fan uses 2 to 3 Watts
C) A typical processor can use 51 to 125 Watts.
Depends on what processor it is.
The Acer Aspire M1100 series processor options, are either an AMD Athlon 64 X2, or an AMD Athlon 64, or AMD Sempron.http://en.wikipedia.org/wiki/List_of_AMD_Athlon_64_microprocessors
The highest wattage usage is 89 Watts. (TDP. Thermal Design Power)
You can test the power supply. A multimeter, or power supply tester is required. (Average cost for an inexpensive multimeter is around $12. Auto parts stores are one place these can be found. An inexpensive power supply tester can be purchased for around $20)
You can also replace the power supply with a known to be good unit, if you happen to have one around, for a test.
Has to have at least 200 Watts. The correct amount of power cables, the correct form factor, (ATX), and at least the correct amount of power cables.
If you would like guidance in testing your power supply, or replacing, simply state so in a Comment.
Four: I'm not knocking Acer computers, but they are a budget line of computer. As such they use low quality parts.
The Electrolytic Capacitors on the motherboard are one such component.
In particular, it is the Electrolytic Capacitors used on the motherboard in the Voltage Regulator circuit, that should be paid special attention to.
If you are not familiar with electronic components, nor the Voltage Regulator circuit, the above will look like a foreign language to you.
[Understandable. Not everyone wants, or needs to be a computer 'geek' like myself]
Processor operate with a specific voltage range. This voltage range is very small, and cannot be exceeded, nor limited.
The motherboard voltage regulator circuit regulates the voltage for the processor, and also for other components on the motherboard.
There is more than one Electrolytic Capacitor used in a motherboard voltage circuit. If just ONE capacitor is bad, the processor will not work.
The following is a guide for visual failure of capacitors.
This information will help explain Electrolytic Capacitors, what they look like on the motherboard, and the reason why they fail.
If you find the information is not concise enough for you, or you would like a less detailed explanation, simply state so in a Comment. I'll be glad to explain.
In an additional comment, I'll post a link to information on the motherboard voltage regulator circuit.
If you have any questions concerning anything I have detailed here, or would like more of a breakdown, simply state so in a Comment.