PC fails to boot – no POST

I have a Compmaq PRESARIO 5304 [300mHZ processor] that was failing -crashes, lockups, bad sectors – on which I replaced the hard drive. Worked fine for 6 weeks. Yesterday, when it booted up, the screen flickered as though the power input were varying, then there were fine black “dots’ all over the screen. When I touched my mouse, the dots became multicolored & the system locked up. When turned on, the power light is the only thing that came on [I can hear the fan] & I had to unplug it to turn it off. Left it set overnight & now when turned on, after about one minute, it turns its’ self off.
HELP?