Does it work any better to download a full installer from this page:

https://www.mozilla.org/firefox/all/ (scroll down to your preferred language)

If not, what is the specific wording of the error message you get?

your current security settings do not allow this file to be downloaded

You might need to change a setting in IE: http://answers.microsoft.com/en-us/ie/forum/ie8-windows_other/error-message-your-current-security-settings-do/59cc236d-7baf-4552-92ff-b34b9a6942aa

Regarding the crashing... Were you getting the Mozilla Crash Reporter dialog, or the Windows crash dialog? If you were getting the Mozilla Crash Reporter form, your Firefox may have logged some data that would help track down the cause of the problem. You can submit that data to Mozilla and share it with forum volunteers to see whether it points to the solution. Please check the last section of the support article "Firefox Crashes" for steps to get those crash IDs from the about:crashes page, and then post some of the recent ones here.

Depending on stability, you might need to start Firefox in its Safe Mode. That's a standard diagnostic tool to deactivate extensions and some advanced features of Firefox. More info: Diagnose Firefox issues using Troubleshoot Mode.

If Firefox is not running: Hold down the Shift key when starting Firefox.

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any less crashy?