It's not under your Program Files folder, it'd be under your user account's AppData folder.
C:\Users\<username>\AppData\Roaming\Liberty BASIC v4.5.1
It's a hidden folder, so unless you turn on the option to show hidden files, you won't see it if you're manually navigating through your hard drive.
Quickest way to get to the AppData\Roaming folder is to type %APPDATA% into the Windows Search bar on the taskbar, making sure to include the percent signs. It should show a folder result; when you open that result, you'll be in your AppData folder, and there should be an LB folder in there that contains the error.log file.
Error.log file
----------------------------------------------------------------------
Liberty BASIC will log hard errors in this file. This means that as a
user of Liberty BASIC, you will probably not be able to understand
much of what you read here. More than anything, this information is
useful to the makers of Liberty BASIC. When you have an error notice
that mentions it has added information to this file, please make sure
to gather this information when reporting a problem to Shoptalk
Systems. The information has date and time information, and new
information is always added to the end of the file, so you do not
need to send the whole file, but just the part related to the problem
you are experiencing. Send a detailed explanation about how to
reproduce the problem along with a small example program if possible
and also the error.log information to support@libertybasic.com
Thanks!
Error log timestamp Wednesday 21-07-14 11:16:39 PM
Runtime error: error closing key
Error(Exception)>>defaultAction
Error(Exception)>>activateHandler: <anUndefinedObject>
Error(Exception)>>handle
Error(Exception)>>signal
Error class(Exception class)>>signal: <'error closing key'>
RegKeyHandle(Object)>>error: <'error closing key'>
RegKeyHandle>>close
RegistrationDatabase>>close
RegistrationDatabase>>includesKey: <'V亁?C;==;>='>
RegistrationDatabase>>at: <'V亁?C;==;>='> ifAbsent: <aBlockClosure>
RegistrationDatabase>>at: <'V亁?C;==;>='>
[] in RegistrationDatabase>>values
[] in Collection>>collect:
OrderedCollection>>do: <aBlockClosure>
OrderedCollection(Collection)>>collect: <aBlockClosure>
RegistrationDatabase>>values
Basic class>>usernameFromRegistry
Basic class>>loadRegistrationFromRegistry
Basic class>>loadRegistration
Basic class>>start
[] in SessionModel>>startBasic
ProtectedFrameMarker(BlockClosure)>>setUnwind: <aBlockClosure>
BlockClosure>>ensure: <aBlockClosure>
SessionModel>>startBasic
Message>>perform
NotificationManager>>empty
NotificationManager>>runPendingEvents
NotificationManager>>runEventLoop
Message>>perform
Message>>evaluate
Process>>safelyEvaluate: <aMessage>
Process>>evaluate: <aMessage>