Could be. You don't say which Dimension you have, but the battery tends to be a CR2032. If you take the battery out, it will forget the date. It may forget anything between nothing and everything, depending on the motherboard model. I don't know for Dell. You may want to write down any non-standard settings you've made in BIOS, if any.
But yes, it's probably the battery, and it's probably easier to replace it ($4) than test it. The date is a bit of an odd one though.