trust me, it'd be better and cheaper for you to do it yourself. Repair are not cheap because of the labour hours needed to diagnose a fault and correct it.
First try a hard reset: take out the battery and power lead, and press the power button for at least 15 seconds. Replace battery and lead and see if it turns on.
Pull out the HDD and run hdd tune health test on another computer. Try with one RAM stick/switch slots and try different RAM all together.
Remove the back cover, and remove the CMOS battery to reset the CMOS.
If this doesnt work, open her up and look for loose screws or things that may be shorting it. Check for dust around the HSF.
If this fails, take out the mobo, reseat the HSF and check the GFX chipset to see if anything has burnt out. To be honest the problem doesnt sound too serious though, if its showing the BIOS screen then at least you know a lot of the key parts are functional.