Maybe, maybe not (about the disk space, not Mary being here). Sorry if I'm being pedantic with the below, no offense is meant.
Low disk space might slow things down. A lot of the images used to display a page get stored on our computers. The less and less disk space available, the more different locations on the disk drive they are stored. The computer makes a list of where they are stored, then consults that list and goes looking for them every time a new page is loaded. The less free space available, the more 'looking' needs to be done. That's probably why some folk are having some slowness issues today.
It kind of like what would happen if your grocery store delivered your groceries while you weren't looking and put them away for you. If your kitchen is full, they could put the corn in the washer, milk on the back porch, cookies under the bed and pasta in the shed. If they left a list, you could find them but it would be a slow process. So, what would you do to avoid this (other than call the police)? You'd probably clean up a bit, group similar foods together to free up some space, so that the next time the groceries were delivered they could be put all in one location and you would be more likely to find them quickly. Getting back to computers, you are the computer and the groceries are the images. The kitchen is your hard drive. Deleting old files and then defragmenting the hard drive is what would be done to speed things up. It's not a difficult thing to do, but can be a nervous situation if you arent' accustomed or are unfamiliar.
Another reason for slowness might be that it is taking a while to store all of the new images (headers, banners,backgrounds, etc.) for the first time. If disk space is not an issue, things should speed up a bit over time.
Last, if memory is the problem, if you know anyone technically inclined (16 year olds are great), you could ask them to help you purchase and install some more memory in the computer. The older the computer, the cheaper it is.
Again, I'll apologize if this comes across as high-handed and (I hope not) condescending. I might have told you less than you already know. My goal is to be of help, and if I've not done that please feel free to say so. And please, there is no need to mince words.