If he'll mechanically secure those wires so they want to lay right on the pads where he wants them soldered he can make it work. I'd drill a hole nearby and use cable ties.
All this has been said before - here it is in one place , no offense intended to anybody:
Three rules of soldering:
1. Cleanliness - you should see bright copper or bright solder
2. Make the joint heat the solder not other way around
3. Dont rely on solder for mechanical connection.
A little flux will help the solder flow. You want "Rosin Core" solder which has flux in the middle. NEVER use acid core on electrical stuff, that's for plumbing.
When soldering two wires together,
1. clean them
2. twist them together, or provide something to hold them together
3. Heat them with iron on one side, touch solder to other side of joint . Solder will flow toward the source of heat. When it flows, remove heat and don't let wires move until well after solder freezes.
When soldering wire to a PC pad:
1. Get the wire held where you want it by some mechanical means - nylon cable tie, string, hotglue, wedge it under a nearby part...
2. Clean and tin wire if not already so
3. Apply heat to pad and wire simultaneously, when solder on pad melts push wire into molten solder and remove heat.
i think your biggest trouble is not making the work heat your solder.
Use SMALL solder - my favorite is Kester 44 , 0.031 dia.
http://www.kester.com/SideMenu/Products/HandSolderingMaterials/CoredSolderWire/tabid/259/Default.aspx
there's a product called Solder-Wick or Chem Wick that's handy for removing solder from circuit pads, see this video
http://www.ehow.com/video_4435740_use-solder-wick-remove-solder.html
and if you figure out how to block those %*U^$@#$ pop-up ads please let me know.