How are you trying to gain access to the registry? Are you using Run > Regedit, the Start menu search box > Regedit, or something else? Try using the Start menu search box > type in regedit > then right-click regedit.exe > run as administrator. Click "yes" on the UAC prompt. Does that get you into regedit?
I think it will be difficult to say for sure if your machine has become infected. Some malware can be so deeply embedded that even reputable anti-malware tools may not find them. However, the more anti-malware scans you run that come back clean, the greater the probability your machine
isn't infected. (But I would never say it's a 100% guarantee.

) Some of the free tools suggested in this forum include:
Malwarebytes
Hitman Pro
ESET Online Scanner
Superantispyware
Windows Defender Offline (not to be confused with other Microsoft products with similar sounding names.) Or from the
Microsoft site.
It's also possible your problem may not be malware related. Your computer may have damaged or corrupt system files that are preventing you from gaining access. You could run a system file checker scan from an elevated command prompt (option two.) If problems are found run the scan 3 times rebooting in between each scan.
http://www.sevenforums.com/tutorials/1538-sfc-scannow-command-system-file-checker.html
You could also try accessing Advanced Boot Options and run in Safe Mode. See if you can access the registry that way.
http://www.sevenforums.com/tutorials/666-advanced-boot-options.html
If still no joy I'd try a clean startup (AKA clean boot) to see if you can isolate a specific application that might be causing the problem.
http://www.sevenforums.com/tutorial...ation-conflicts-performing-clean-startup.html
There are other troubleshooting steps you can take as outlined in this tutorial prepared by one of the Forum experts.
http://www.sevenforums.com/tutorials/220165-troubleshooting-steps-windows-7-a.html
Hopefully something here will solve your problems or provide additional information to offer additional suggestions. Please post back how it goes.