With old coax the things you're most likely to see are UV degradation of the insulation and water ingress.
Visually inspect the insulation, looking for cracks when bent. If this cable was not exposed to the sun, it's probably fine in this regard.
Water ingress will show as corrosion on the conductors, an increase in loss, or a change in characteristic impedance. The ends are most susceptible, so remove them if the shield appears corroded. For the outdoor end you might consider removing a couple feet more to be safe. There may also be nicks or fine cracks in the insulation that allowed water to enter which you may not be able to see.
Put a dummy load on the far end of the cable, and check with an antenna analyzer. The SWR should be flat over the entire range of the analyzer. If you don't have an analyzer, a directional coupler in conjunction with a signal generator or low power transmitter works also.
To check for loss, you can make a simple RF detector to measure the peak voltage:

simulate this circuit – Schematic created using CircuitLab
Use a Schottky diode for best sensitivity, though an ordinary silicon diode like 1N4148 may work well enough. Keep the leads between the resistors, diode, and capacitor as short as possible. The voltmeter can have long leads since it's measuring DC. Ordinary 1/4W resistors are fine as long as testing is limited to low-ish powers (<10W) and brief (a couple seconds) periods.
I build it into a BNC connector. This one worked fine at 440 MHz:

Measure the power directly from your antenna analyzer / signal generator / low power transmitter. Then put it on the end of the coax, and measure that. Power is proportional to the square of voltage.
$$ \text{loss (dB)} = 20 \log_{10} \left(V_\text{in} \over V_\text{out}\right) $$
If the cable passes visual inspection, SWR test, and loss test, it's fine to be reused. And you'll also know the loss, so you can decide if it's worth getting some better coax.