Much of my mispent youth, aside from my obsession with photography, was spent turning wrenches on rusty screws on cars. One of the most amazing things to me, when I eventually began making enough money to afford them, was how a small air-impact wrench could make many (not all) seemingly hopeless screws (bolts, if you will) virtually jump out of their rusty holes. Now this is unworkable on small screws as they just snap off on the first impact.
But there is now another class of impact driver that looks like a cordless drill, and they can do the same magic on smaller screws. I wouldn't use mine (an older 12 volt model) FORCEFULLY on anything much smaller than roughly an 1/8 inch nominal screw diameter, except as a last resort, but may be worth trying if one of your friends has one. The lower voltage ones have less torque, which is what you want for smaller screws.
Note that I used the word "FORCEFULLY" above to mean squeezing the trigger all the way. The impact mechanism doesn't start until there is enough resistance and you squeeze the trigger hard enough.
Most of the people I know have never used an impact driver, so a few words on them. First, there is very little back reaction on your hand, and second, if a Philips screw head is getting damaged such that a regular screwdriver wants to "cam out" (you have to press very hard to keep the screwdriver from slipping), an impact driver is barely affected by this. You need very little pressure to keep an impact driver in the screw head. The first time you use one they just seem like magic.