This sounds similar to something I ran into in the past on a bad patch attempt. User had patch issue that broke during attempted install. ALM service would start, but the icon would always error out. Ran deployment wizard and had similar message about the qcsiteadmin_db not being accessible.
In the past case, qcsiteadmin_db went SUSPECT. This is a marking next to the database name in SQL management studio that indicates possible corruption and takes the DB offline essentially.
This was discussed in an answer on EOT found here: [past article]
As you mentioned you can log into SQL server, assume you mean SQL Management Studio. Do that again and expand out your Database folder. Find the qcsiteadmin_db in the list and see if at the far right it says SUSPECT. If so, lets try the repair then on the DB as I mentioned in the previous post.
Here is a full example, so try below. Sometimes copy/past works, but if not, advise you manually type in the commands in a New Query window.
EXEC sp_resetstatus qcsiteadmin_db;
ALTER DATABASE qcsiteadmin_db SET EMERGENCY
ALTER DATABASE qcsiteadmin_db SET SINGLE_USER WITH ROLLBACK IMMEDIATE
DBCC CheckDB (qcsiteadmin_db, REPAIR_ALLOW_DATA_LOSS)
ALTER DATABASE qcsiteadmin_db SET MULTI_USER
The above uses qcsiteadmin_db as the name as that is what you said your db's name was. If it repairs, the output of the query should tell you that the db now has no issues for the CheckDB.
Can try F5 for refresh of the view or log out and back in for SQL Management Studio. SUSPECT should be gone. If you see SUSPECT on any other databases, modify the query and put in the database name. Before I had seen it for both qcsiteadmin_db and for a couple of individual project databases.