Unlikely to be the LCD screen, IMO.
It may be the inverter, or the cold cathode tube, or else it may be a problem with the graphics chip output, or a problem with a connector, but since it starts off OK from cold or sleep, it may be a symptom of overheating. Overheating can affect the voltage stability of the whole system, with unpredictable results.
Laptops are prone to overheating problems, due to having to fit all the components in a small space, and it only takes a little fluff/dust to clog the heat exchanger. Overheating problems often start after only a few months use.
The three components that generate a lot of heat are the main processor, the Hard drive and the graphics processor chip. Most laptops use a heat pipe to transfer heat from both the graphics chip and the main processor to the heat exchanger, over which the fan blows cool air. The graphics chip is invariably further along the heat pipe than the main processor, thus can suffer from the effects of an overheating main processor, even if it is not overheating itself.
Some laptops are easy to remove dust build-ups - the fan assembly is located under one of the covers that provide access to the memory modules or the hard disk.
Other laptops require almost total disassembly to get to the fan and heat exchanger. The Vostro, sadly, appears to fall into this category. Here is a blow-by-blow guide:
http://www.insidemylaptop.com/take-apart-dell-inspiron-1720-1721-dell-vostro-1700-laptop/
Back up any essential data before attempting to disassemble your system!
Your laptop may run cooler under safe-mode conditions to enable a complete back up. Command prompts (DOS screen) do not utilise much graphics processor activity.
Remember that the screws are small and easily lost, so have the right screwdrivers handy, and somewhere to keep all the parts safe. I use a white plastic tray and Blu (or White)-Tac to keep the screws in the right positions and order for replacement. Also, the separated bits of laptops are often quite fragile, and easily damaged when removing and replacing.
Another tip is to take digital photos of key stages of the disassembly and layout of the removed bits, so that if you are interrupted, you can recap exactly where you had got to, and to aid the process of reassembly.
The usual advice is to use a can of compressed air to dislodge the debris. If you have allergies or any respiratory problems, do this only in a well ventilated area. Vacuum cleaners may damage delicate components.
Dust is sticky - a small fine bristle paintbrush will dislodge more dust in crevices than compressed air alone.
Finally, you are probably invalidating any guarantee by opening the case, so make sure that you can't still get a free repair before attempting any of this.
Good luck!
