|Just in case you don't understand the above, let me explain. All motherboards have a small battery (usually a lithium coin-type) on the board that maintains a charge to the CMOS memory chip when the computer is in the powered-off state. The CMOS chip stores all the motherboard hardware settings, including the date & time. If the battery goes dead & the computer is powered off, the settings stored in the CMOS memory are lost & they return to the original default settings.|
You didn't post your motherboard make/model or the make/model of your system, but if the date is defaulting to 2001, you apparently have a system that's over 10 yrs old. Anyhow, what you're going to have to do is shutdown the system, unplug the power cord, open the case, then locate the CMOS battery on the board. It looks like this:
Get the model number off the battery, then buy a replacement. The CR2032 is one of the most common. You should be able to find a 2-pack for under $5. You don't have to go to a computer shop, you should be able to find one wherever batteries are sold.
Once the new battery is in place, boot the system & enter the "other mode" that you mentioned. Correct the date, time, & other settings, save & exit.