If you are trying to access computer, that has only one account, without password, you'll be asked to provide password anyway. This is normal. By default, Windows blocks all non-local logins to accounts that don't have passwords, for security reasons. There are few things you can do with this situation.
1. If you are in the same workgroup, create identical account (with no password) on the machine you're connecting from.
2. Secure destination computer's account with password and use it, when prompted, if this is an option for you.
3. If you're using Windows 7 or newer, add both computers to Home Group and you'll be able to access them without password.
secpol.msc command and dig through security settings there to find the one, that blocks non-local access to accounts without passwords. Note, that there are hundreds settings in
secpol.msc, so you waste some time before you find it. Note also, that this is not recommended solution, as you're lowering already low security defences on your Windows.
First option is best one, whenever you can apply it. Using the same account / user name (with or without password) was proven many times to work in situations like that. And assures the biggest stability of mostly weakly implemented networking in Windows. If you can, always use the same user name on all machines, you're trying to access via network in Windows.