I made some changes to my translation based on what a native said to me in the "Hi Native" site. I'll leave his comment here for reference:
"First of all, ❝ゆるがない❞ is ❝waver❞. So, I should change ❝I won't forget what he had before❞ into ❝I won't wavered what I was there❞.
Second, ❝痛み 記憶❞ is not painful memories. These are divided into pain and memory in japanese.
Finally, I feel that ❝守りたい 願いは 残る 希望になって❞ has will. Therefore, it becomes ❝I want to keep wish and it will become hope❞.
I am not good at writing English because I'm a japanese. But, I think that this translation is almost correct. And, I am fun to write this reply to you, Listening
"想いのゆくえ" by Nana Mizuki (水樹 奈々).That's all. Thank you for reading my reply and Keep going!!"
It seems that his English is not so good, so I left the second line as it is until someone more fluent corrects me, but I'll take the advice on the ❝痛み 記憶❞ part. I think he's right, there are no particles there, so maybe they are just separate words. Also I'll add the "I want to keep" to the ❝守りたい 願いは 残る 希望になって❞ line.
Source: https://strongtomorrow.wordpress.com/romanized-lyrics/tales-of-symphonia...