A failing PSU can cause all sorts of oddities. Your 475 watt just barely meets the minimum specs for the 5870 as it is. And yes they do lose efficiency over time.
The thing is, it's the heart of your system. Buy a GOOD one now and it will last a long time and give you peace of mind, even if it's not the cure.
#1: Phenom II C2 955BE @ 3.6, Antec Kuhler 920, Gigabyte GA-MA790FX-DS5, Asus 5870/V2, ASUS Xonar D2X, 4 x 1gig OCZ2N1066SR2GK @800, Antec Truepower New 750, Arc Midi, Vistax64
#2: Athlon 64 X2 4200+, AGP 1950pro, Audigy 2, Asus A8V-D, 2gig ram, Enermax 465P, Antec900case. Now on Win8.1pro cat 10.2