Error installing SQL Server

Yesterday I installed SQL Server 2014 onto a Win2012 server that has already SQL Express 2014 installed. I uninstalled/reinstalled it three times, but to no avail: The server wouldn't start after setup.

In SQL Server Configuration Manager under "SQL Server Services",

• SQL Express gives "Log On As" as "NT Service\MSSQL$SQLEXPRESS"
• SQL Server gives "Log On As" as "NT Service\MSSQL$SQLSERVER02"

When I change that to INTRA\Analysis Services, the sql server starts, but won't let me log in ("sa" with correct password fails, and the installing Administrator account fails as well). Now, when I change it back,

• SQL Express accepts "NT Service\MSSQL$SQLEXPRESS" and auto-fills the password field
• SQL Server rejects "NT Service\MSSQL$SQLSERVER02" with the message "WMI Provider Error" - Cannot find object or property. [0x80092004] "

Using that error message, I found this proposed solution. But this did not solve the root problem. In my despair, I tried to start "ImagePath" property manually from shell while logged in as administrator, which lets the server start.

Login still fails, but every time I try, I get the following error message in the shell:

2015-05-13 11:09:37.39 Logon       Error: 18456, Severity: 14, State: 5.
2015-05-13 11:09:37.39 Logon       Login failed for user 'INTRA\Administrator'.
Reason: Could not find a login matching the name provided. [CLIENT: <local machi
ne>]

Now, what does that mean? (yes, INTRA is our domain and "Administrator" exists and is an admin account; I am logged in with that account at the server right now and didn't have to provide credentials to SQL Server manually, since this is handled by SSMS for me.)

EDIT: (SSL cert errors have been resolved, but the main problem remains)