Hm...
Restarting randomly, for me, often implies a loose heatsnik that forces the system to restart/shut down to avoid damage. Here's my fairly trusty checklist on dud boxes:
1.) Heatsink is properly attached, therefore fully capable of distributing processor heat.
2.) RAM is a known stable stick. (Always troubleshoot with one stick at a time.)
3.) Nothing is shorting your motherboard. Screws and other small metallicy stuffs can fall between motherboard and case, creating many an electrical issue. Heatsinks are known to short boards. (Drastic measures involve removing board and components from case, laying on carpet/foam to test the shorting possiblity.)
4.) Your motherboard is fried and corrupt due to prior power issues--look for bulging capacitors or burnt plastic around the power connectors. (Many dead motherboards, however, are not apparently dead and need to be tested through this checklist to find defect.)
5.) Your motherboard is not currently receiving proper power, resulting in random boots and no bootup at all. (Many computers as of today should have 300watt-350watt minimum power supplies to avoid lack of juice. Antec = well approved manufacturer.)
5.) Monitors are rarely the problem, but it's always good to test a machine on another monitor to ensure results.
6.) A peripheral can cause the issue: Take out anything that doesn't produce your video. (Naturally, video cards can die, so you'll need another working machine to test these devices in before pronouncing dead.)
7.) Easy; make sure everything is connected nicely. :cheesy:
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Now, you say you've checked a lot of your hardware. I'd point at your motherboard and call it something vulgar.