I would avoid repeated freezing and thawing of the PCR reaction components (best is to aliquot them). Personally I have never used components that have passed their expiry date, but I would guess that their activity (especially enzyme) would decrease with time. This depends how old your enzyme is. Regarding your sample storage, I would just briefly check its quality to see if it hasn't degraded (just to be sure), so simply run NanoDrop it will give you relative information about its quality in storage.

For those cases its always helpful to run a positiv controll alongside (a template under conditions that always results in bands).

For the DNA extraktion you can have a quick look via Nanodrop. Collect different flowthroughs to figure out if on any step are a higher amount of DNA get washed of (if the kit uses a column).

Yes, these components are viable for a long time in -80 celcius degrees, but try to alicuotate the components in small cuantities ready for use, maybe in vials. By this method you will avoid freezing and defreezing, that can cause the deterioration of these compounds.

I agree with Fabian, run the old reagents on samples that you know would work; that will indicate if it's the samples or the reagents, or both, that are spoiled.

Nanodrop will indeed give you a look at quality. If it's a plasmid you are trying to use as a template, you can also run it on a gel. If you get a smear, it's degraded.

I've used very old reagents and found them to still work.

Agree with everyone else but want to add something about "not getting any bands at all" which may be related to the DNA you are trying to amplify. For example, high GC DNA, which you may have trouble amplifying using a regular polymerase. 

Storing your DNA or PCR reaction mix at -80 oC will not affect the integrity of DNA or the activity of enzyme if they are not frequently thawed. What was the concentration and purity of the DNA used? Did you check the Tm and delta G value of your primer? If not, just check them and go for gradient PCR or touch down PCR. 

I worked with older samples stored at -80C and everything was fine, something else might be wrong