If removing one RAM module solve the crash but make the computer slower, it probably mean that you have dual channel memory and one module is defective.
You may try replacing BOTH RAM modules. If possible, get modules that are as big as the motherboard can support and in your price range.
Dual channel memory normaly gives you about twice the data bandwidth and partly circumvent the addressing latency. It's similar to a hard drive raid 0 setup, but for the actual RAM.
Higher bandwidth means faster access to the content, and make the computer faster. It's the most obvious when you access large amount of data.
For the problem deleting or renaming files, do you get any error message?
If it say that you don't have the authorisation to proceede, you probably lost the ownership of your files.
In some cases, a memory problem CAN cause that problem. It's also the case when you take a drive from one computer and transfert it into another one, or you do a reinstall of the operating system in any multi-drive or multi-partitions setup.
In Windows 7 (similar in XP, but the content and buttons are different and not in the same locations, don't know for Vista).
Right-click a folder for whitch you have your problem and sellect "Properties".
Chose the "Security" tab.
Click the "Advanced" button.
In the new window, chose the "Owner" tab.
You should have a "Take ownership" button or underlined link. Click it. Sellect Yes/OK.
It can take a while if there are a few thousands of files in many sub-folders.
Close this window.
Next, click the "Modify" button.
If there are any "user" identified by a string of leters and numbers, you should delete those. You NEED to be logged in as ADMINISTRATOR do perform that task.
Repeat the process for any folder presenting the problem.
Electro, April 2013