"when do you congujate the verb or adjective before ようだ and らしい in negative or in past or both, and when do you conjugate NOT that verb or adjective, but instead the ようだ and らしい"
The crux of this is similar to in English -- what do you want to say?
Let's look at the past tense first.
- It seems he is going.
- It seems he went.
- It seemed he was going.
- It seemed he went.
For 1 and 2, the "seeming" is in the present tense, so we know that whoever is thinking about this is thinking about it "now" in the present (relative to the temporal context of the utterance or text).
For 3 and 4, the "seeming" is in the past tense, so we know that whoever is thinking about this is thinking about it "then" in the past (relative to the temporal context of the utterance or text).
For 1 and 3, the "going" is in the present tense (specifically present progressive), so we know that "he" appeared to be going at the time that the "seeming" occurred (at that point in time that the person thinking about this, was thinking about this).
For 2 and 4, the "going" is in the past tense, so we know that "he" appeared to have already gone, some time before the "seeming" occurred (before that point in time that the person thinking about this, was thinking about this).
In Japanese, these four might be rendered as:
- 彼は行くようだ。
- 彼は行ったようだ。
- 彼は行くようだった。
- 彼は行ったようだった。
This is simplified somewhat for purposes of illustration -- Japanese tense is sometimes used slightly differently than in English, so strictly speaking, usage patterns will not match up one-to-one as cleanly as above, but this should give you a general idea.
This works out similarly for negative -- did something "not seem like X" (Xのようじゃない), or "seem like not X" (Xじゃないよう), etc.? Figure out the sense you're trying to convey, and phrase your Japanese accordingly.