Hi skorpius,
It sounds like there are a few issues here that could be examined separately. And some more info about your present system would be helpful. For example, how is your storage configured? (e.g. RAID 1, RAID 10, RAID 5, other?) Your DBs are small, but storage config can have a big impact on performance (especially RAID 5, in my experience).
DB clients: are they local? Remote? A mix?
DBs: You mentioned three applications; is it one DB per app or multiple?
Printing: how is this configured? Is your DB server also a printer server, or are you printing to resources on another print server?
Denied logins: does this mean application login? Database? OS?
"Slowdowns": how are these observed? I/O throughput reduction? Perceived reduction in client application performance? CPU spikes on the DB server? Your standard IT checklist applies here: look at the processes on the "slow" system during "normal" performance, and again during "slow" performance; look at CPU usage and disk and network IO. If it is a client/server app that is slow, add in network tracing, both before and after (Wireshark/tshark/tcpdump/your tool of choice). Also, it this box dedicated to these three apps or does it host other apps?
Network: if this is a client/server app, have you confirmed that your link speeds are what they should be, and full duplex? Does your network carry any significant load apart from your production traffic (batch file transfers, etc.)?
And probably the biggest question: based on your anticipated migration time to the new platform, and the severity of the current issues, is there value in trying to determine their root cause? I hope this helps.