What kind of password did you enter, a BIOS password or a Windows password?
Just in case it was the BIOS password, see if anything offered by https://www.google.com/search?q=dell+studio+1735+bios+password+reset
helps you or a local repair shop to fix it.
Just removing that battery, by the way, might not be enough if the normal battery is in. That provides more than enough power to keep it active.
I'm sure you can file your court papers using another PC or laptop and the needed files from your backup or from the hard disk of this now unaccessible laptop (if you take that out). No need for any stress.