Are there any forms of brain damage that would leave someone with severe memory loss, unable to speak, or at least do so intelligibly, and with trouble moving around, but still able to understand speech and capable of literacy? If not then the priority of traits are as follows; Inability to speak and severe memory loss. Able to understand speech. Trouble moving around (is actually very important to the plot but I can come up with another reason if necessary). Capable of literacy. In the interest of full disclosure and avoiding confusion I should mention that there's a lot of sci-fi stuff in play (long story short, a character suffered severe brain damage, far more severe than what would be necessary to cause the above, and someone else tried to fix it but didn't manage to fix everything) so things probably don't actually need to be completely realistic. That said, I want to try to keep things at least in sight of realism, if only the minimise the amount of handwaving I'd have to do. Also, what would be other symptoms that it'd make sense for someone with an imperfectly repaired brain to have? I'm aiming for the character in question having a level of functionality that's high enough for them to look after themselves and mostly function independently (emphasis on "mostly") but low enough for those who used them as a human guinea pig under ethically dubious circumstances to regard them as a failure.
These are typical symptoms of an ischemic stroke. My father had one (or, more accurately, a series of them) that damaged his speech, several motor functions (balance, swallowing, eye coordination), and his ability to read, but left him otherwise as sharp as he ever was. Therapy allowed him to recover much of what was lost, including learning to read all over again. He died of a second, more massive stroke that left him brain-dead about a year and a half after the first one. The nature of stroke as a literary device is that you can tailor it to your character's needs and still remain within the realm of probability. My father's "stroke" was caused by clots that starved various parts of his brain of oxygen, and those areas were pretty random. He could have been spared the reading damage, or the swallowing damage, or he could have other parts of his brain impacted. Other symptoms might have been blindness, deafness, local or general paralysis ... you name it, and somebody at some time has had it. There's a lot of material on ischemic stroke around. Start with https://en.wikipedia.org/wiki/Stroke and go on to more specialized sources.
To be honest I hadn't considered a stroke as the cause of my character's messed up brain, probably because of his age. I've always thought that strokes were usually something older people had and my character is young, less than twenty at the time that whatever happened happened.
I had a 4 yr old child in the ED that had had a stroke. He complained his tummy hurt. Turned out it was his chest (heart) that was causing the pain and that had led to the stroke. The doctor was great though he didn't know what the kid had, he picked up on a left sided weakness that I think a lot of doctors looking at a kid with a belly ache would have missed. But I digress: There are lots of good resources about stroke aftermath. Here's a good starting place: http://www.strokeassociation.org/STROKEORG/
Addressing the language and literacy part specifically: Inability to speak (or great difficulty speaking) combined with the ability to understand speech is known as Broca's aphasia. The most common cause is indeed stroke, though other brain injury can also cause it. People with Broca's can usually read, but have the same trouble writing as they do speaking. In other words it's an issue with expressing language in any form. The part of the brain that relays information from language centers to the motor cortex is damaged--so thoughts are still going on, they just can't make it to your mouth and hands. As for the "imperfectly repaired brain" thing, try looking up symptoms of traumatic brain injury (TBI). There are a number of issues that tend to linger around even when a person has largely recovered.
