I am sorry that your last post was overlooked.
The answer to your question is, no, your machine is not trustworthy for banking nor any other secure transactions.
Backdoor Trojans are the most dangerous and most widespread type of Trojan. Backdoor Trojans provide the author or "master" of the Trojan with remote "administration" of victim machines. Unlike legitimate remote administration utilities, they install, launch and run invisibly, without the consent or knowledge of the user. Once installed, backdoor Trojans can be instructed to send, receive, execute and delete files, harvest confidential data from the computer, log activity on the computer and more. These Trojans may also alter settings in order to allow a way back onto a system in the event they should be removed. There is absolutely no way to check all the possible settings that may have been altered by such an infection; therefore, there is no way to ascertain the safety of a machine once its security has been compromised by a backdoor Trojan.
The only way you can be certain your system is safe after having been infected by a backdoor Trojan is to reformat the hard drive and reinstall the operating system. Data can be saved, but neither programs nor executable files of any sort should be saved as they may very well carry a hidden infection. As this issue appears to be resolved, this topic is now closed.
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