Yup! Sounds like a low amperage/voltage to the solenoid.
As Clark pointed out, a high resistance connection can cause this, so it would be prudent to check, clean and tighten the connections (a known common problem).
You can take the battery to most auto parts stores or and have it tested. Battery Plus will do this too if you have one near you.
These batteries should be kept on a tender when not being used for long periods, and especially in cold weather.
You can try putting it on a charger for a day to see if that brings it back to life.