First up, if you've have old games inside your HDD, chances are you're not going to get them booting up directly, you have to re-rip or re-FTP in them in.
Secondly, make sure you have the original eboot.bin + param.sfo for all your games, it improves compatibility between all backup managers.
Thidly, and this is the most important of all, make sure you fix your permissions. When FTP-ing with filezilla or many other backup managers, most FTP software break file access permissions to the entire folder of the game. What this means is that you need to either run rogero manager which will detect and fix the permissions (after fixing you should be able to run in any backup manager) or run the fixpermissions.pkg available from some other sources in the forums.
If you're stuck on a black screened game, heres what i'll do. Delete all traces of it on the internall hdd, reftp or re rip the games, ensure i have the correct original eboot.bin + param.sfo, run rogero manager first time, enjoy.
So far i've gotten Black ops, GT5, RDR and many other games working fine. If you're having problems patching games, you can try downloading the patches externally using (Another New Update Software) and installing them separately.
Also, downloading your games gives you many problems. Most scene releases contain modified eboots + files, rendering them useless. Rip your games from legit BD's!