Error 0271 probably means your computer lost all power, and lost the time/date. Just press F1 the second anything comes across the display and it should start the BIOS setup utility. Set the date and time, and let the battery charge awhile.
Error 2010 is another pain that I just dealt with. It involves certain machines with a strange bios that looks for firmware that is present in very few hard drives. The easiest way to fix this is to flash the BIOS with an identical bios that doesn't have this error. Here's the link...
Scroll down until you see "Use unofficial modified BIOS". Before you flash your bios with a new one, make sure you check on the bottom for a sticker that says what type it is, and select the corresponding download link. THIS IS VERY IMPORTANT. The bios updates are VERY specific, and if you choose the wrong one, the update will fail and you have to download the other. Just a small time saver.
*Just a little tip in downloading the file. Sendspace also is covered in ads, so before you click any links, look at what the link it is pointing to actually is. If you're not careful, you might end up getting something you don't want, like adware or malware.*
When you download the .zip file, extract all the files to one folder, and click on the "BIOS" icon. It's pretty distinguished. You don't need to change any of the program's settings, just click "Flash". If you downloaded the right one, then no error messages will appear halfway in, and your computer will auto restart with the new bios.
Either way, neither of these errors actually indicate a huge problem. Error 2010 could be a sign, but generally it's because the hard drive isn't the one that came with the laptop in retail packaging. If you don't feel like taking the time to fix these, you don't need to. Your computer clock might be a little messed up, but that's it. Hope this helped!