Can I access my old pictures from my iphone4 on iCloud.com?

The easiest thing to do would be to use a computer and log in to https://www.icloud.com/ and click on the Photos app to check. However, iCloud Photo Library originated with iOS 8.3 and if my memory is correct, the iPhone 4 couldn't have run that.

The other possibility is that the photos on the old phone were included in a backup. You can't log on and view the contents of a backup but you can restore it to a new iOS device.