i think a lot of people believe that there is some sort of colour changing dot in those spots..infact they are on the inside of the phone on the motherboard.
the first thing to do is to open the phone and clean it.. you'll also see the pink dots. Get some isopropyl alcohol.. the higher the percentage the better (90%), and a soft brush to scrub at everything. take the phone apart as much as you dare... just the motherboard and the dock .(you don't have to wash the display..just the connectors)if you don't feel like taking the metal shield off the motherboard you can try submerging it for a while to see if it will soak off any debris under there.
water leaves a lot of impurities behind and causes corrosion you can't see.it may look like white or green webs. the alcohol will evaporate without leaving residue.clean it a few times with drying in between, pay attention to the connections on the board and on the flex. when it's dry reconnect and see if the backlight is fixed..sometimes it's just corrosion on connector 1, but more likely it is the backlight coil-for some reason the 3gs is pretty dainty with this part!
once you've done this the home/power button may decide to work..it just may be they were not making a proper connection. you might get lucky with the backlight!
as for costs.. it depends what decides to work and what doesn't. the home or power flex are easily found and replaced cheaply by yourself, the backlight is slightly more tricky. the part is 6r8 which you can buy on ebay or some online iphone shops for less than $10, replacing it needs a very fine soldering tip and a steady hand. you can pay someone to do it for you..plenty of places advertise for this work.
is it worth it? if you can do the solder yes! and if you can fix the other parts, yes! plenty of people out there will buy this phone in it's current state and repair it.