I'm presuming your PC doesn't POST (IE, Boot up to the Acer logo and attempt to load Windows)?
The problem you describe can be one of two things - either a failing power supply or a fault with your motherboard. To rule out a component, you will need to borrow a power supply from another computer (or from a friend) just to test it out. If the PC boots with the borrowed supply, then the mobo is OK, and your original one is at fault. If it still fails to boot, then the motherboard is the problem.
I'm hoping it's the power supply at fault because they're easier & cheaper to resolve - despite the fact the X1300 is a Small Form Factor PC and uses a non-standard power supply.
A trip to your local PC store should be able to help. Let us know how you get on!
Usually, any power supply will do (providing it is powerful enough for the internal components), but as I've said, the X1300 is a small form factor PC, and their PSU's are much smaller than normal desktop ones. So if you have a small enough supply, then the answer will be yes, otherwise, no!
You can rig up the spare supply just to test. If it still doesn't work, then it's the mobo....