This may be a long shot, since you're not on your usual computer, but do you have the command line tools installed?
aws elb describe-instance-health --load-balancer-name <ELB name>
Returns a list of instances connected to the ELB.
aws ec2 describe-instances <instance id>
Returns among other things the IP address of the instance. If you have your Access Key and Secret Key you can set up the command line tools and skip the AWS console.
EC2 tools: http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/SettingUp_CommandLine.html
ELB tools: http://docs.aws.amazon.com/ElasticLoadBalancing/latest/DeveloperGuide/UsingTheCommandLineTools.html
UPDATE: As of this edit the ELB Command Line tools have been replaced in favour of AWS CLI: http://docs.aws.amazon.com/cli/latest/userguide/cli-chap-getting-set-up.html