To be sure I have this correct, you have a server that has blocked your PC because of port scanning based upon IP address.
1 - Do the server and PC have public facing IP addresses or is this completely on a private LAN?
2 - If they have public IP addresses, is your PC static or Dynamic. In other words, could someone else have had your IP address and used it to scan, which caused you to get banned?
3 - what application are you using to perform the blocking and is it temporary or permanent?
4 - are you running any server applications on your PC that could have contributed to a vulnerability?
5 - can you correlate the time stamps from the logs to verify that your PC was on and had Internet access at the time.
6 - have you run any tools like nmap against your server from your PC which can appear as port scanning.
Now, with regards to checking your PC, the first thing I would do is watch and examine the network connections to see if anything is at work. While your doing this, you should NOT be doing general web browsing because this will open a lot of misc connections, mostly from ads. Second, look at the process tree to see what is running on your system. Three, look for any hidden files, especially in strange areas like /tmp, or /dev.
Here is a link
to the CERT intruder detection checklist. I am posting a link to it because I think it describes some tests you want to run. In particular, you will also want to examine your cron tables very carefully because such an application may wake up periodically.
Here is a set of commands that will give you the process tree and help you examine the cron tasks. The other commands, such as finding files, are contained in the CERT checklist that I linked to above:
ps acxfwwwe, ls -al /var/spool/cron, netstat -anpe