Check the motherboard for bad capacitors, they should all be flat on top, any bulging, leaking, black dots on top is bad, need to replace the motherboard.
Could also be a power supply issue, look for another one to try. Ebay would have some. This computer model is all over the place used also, you may be able to just buy a working full system and swap hard-drives.
Try re-seating the memory after checking for a loose monitor cable. I've had to re-seat memory on a lot of Dell's at work. It should beep at power on if the memory is loose though. Make sure you didn't accidentally press the input button on your monitor and have it now set for DVI when you're connected to VGA or vice versa. If none of those work, you probably have a bad CPU or motherboard. If the power button light is amber, it could be a power supply issue.