My sister gave me her old dell vostro 1400 because it was broken. When u turn the laptop on the back light turns on and the system lights turn on but nothing shows on the screen. I took the laptop apart and found a huge wad of dust in the vent between the fan and the vent. Preventing any air to escape. This makes me think that the cpu is fried. But the fact that nothing shows on the screen makes me think either the screen could be broken or something is wrong with the gpu and yes i checked the memory and the hard drive and it works. i took all the memory out and still nothing showed on the screen. Not sure if i should buy a new processor or a new screen. or even a whole new laptop.
It has an external monitor port. If so, plug it into a monitor and see if it's trying to boot or dead. Specs: Core 2 Duo T5470 (1.6Ghz, 2MB L2 Cache, 800MHz FSB) 14.1” Wide Screen XGA LCD Display with TrueLife 1GB DDR2 667Mhz http://www.notebookreview.com/default.asp?newsID=3873 It's a nice laptop, probably worth money for at least an estimate for repair.
i plugged it into a monitor and even used tv-out. and nothing shows up. she also just told me that she saw green lines go across her screen right before it broke.
If it's beyond your capability to take apart, you might see if there's a laptop repair place in your area that provided estimated/diagnostics for free or minimal cost. A new laptop of comparable configuration is still about $499.00 USD (and only if you're lucky).