If you're not getting a couple volts across each of the sockets, you're not going to get it working reliably and of course they have to be in good shape and let the lamps seat correctly. Socket problems are more likely. It's often the aging poke-in wire traps or sockets that don't stay in place and tend to move away from lamps. The ballast is shot for sure only if you're getting no continuity across the same color leads on a magnetic rapid start directly at the ballast leads. The good old Made in USA magnetic ballast seldom fails in residential use if they're not incorrectly installed. New sockets on freshly stripped wire ends, new 40W lamps and the system should be good for the foreseeable future.
You can still easily find full wattage 40W T12 in retail stores. They all have CRI 87 or higher these days.
This low lumen F40 sold in retail stores is actually a full spectrum lamps tuned at 4100K that emits all the way from near ultraviolet to deep red. CRI is near 90 and R9 approaches 70. Pair these with electronic ballast and you have a excellent quality light that is unmatched by essentially all LEDs out there. This stomps all over LEDs except for very expensive professional color matching products and even those have a spectral flaw between violet and blue. 4100K looks like any other 4100K on white or beige surfaces but colors like strawberries and Ferrari Red are rendered brilliantly along with complex bluish green colors LED lighting can not render. You wouldn't be disappointed. The higher lumen versions have almost the same CRI but R9 is not included in CRI and the R9 on the higher lumen versions aren't impressive.
Since having the highest lumens per watt is not the highest priority in homes, this is a significant light quality upgrade over just about any LEDs you can commonly find today.
You end up getting like 40 lm/W but the CRI is close to 90 with R9 red rendition nearing 70 and this is at a level only the LEDs marketed as super premium critical color rendition will hit. These lamps are not stocked at supply houses, because they're meant for household use only.