+1 with Vertoe, you don't need a new PC per se, you need to re-kick your OS from scratch, if its Linux i would recommend Fedora,Centos or Ubuntu (depending which distro you prefer and i think at present the darkcoin software only works on ubuntu) if its Windows then the latest one that's available i guess, install the latest updates and a good Antivirus + firewall with something like malwarebytes. In my opinion i would install Linux and start learning to use that, its some much more in depth and you get to see almost everything in detail as to what happening on the system. For example if say your system was compromised you could check for any running shell, any interesting connections that may running processes as root on the privileged ports 1 -1024. A simple command such as "netstat -ntlp" will show you what listening on the box, if your looking for active connections just add the -ntlpa flag, if you get more paranoid you could look at doing a tcpdump on your network interface, something like "tcpdump -i eth0" and exclude any known ips whilst taking the packet capture.
Theirs a number of things you can do on Linux to prevent intruders gaining access - like restricting access using software firewall (iptables etc), installing an HDS (host intrusion detection system) etc.. i can also imagine you can do the same thing with windows by restricting access to a certain IP / network range access to your server / computer on a particular port , even enabling NLA access on your windows server should help with the brute force attacks over port 3389 (RDP), just make sure ports such as 135 - 139 are not being advertised to the outside world.
In all theirs numerous server / computer hardening guides out there to help out, however i would recommend that you first harden your pc first then run something like nmap / netcat against your device to see if an intruder can firstly get in on an advertised port and then run something like nessus (vulnerability scanner) against your device to check for any exploits.
I would recommend though the pc that your storing your coins on, try not to browse the web too much on it, as there are websites out there with specially crafted code that can run malicious scripts behind the scenes and comprise your box, i would avoid surfing any *dodgy looking webpages, instead surf using a VM or another device if you have one spare.
I imagine this will keep you reading a bit and hope it helps you in sorting out your compromised box.