<think>
Okay, I need to implement the pack_entries function. Let's see the requirements. The function takes a list of [key, value] pairs and serializes them into a string. Each pair is key=value, joined by semicolons. But there are some escaping rules. Also, there are validation checks: the input must be a list, each entry must be a two-element list, keys and values must be strings, no empty keys, and no repeated keys.

First, I need to validate the input. Let's start with checking if entries is a list. If not, raise ValueError. Then, for each entry in entries, check if it's a two-element list. If any entry is not two elements, error. Then check each key and value is a string. Also, check that no key is empty. And also, if any key repeats, that's an error.

So, for the validation part:

- Check if entries is a list. If not, raise ValueError.
- Iterate over each entry in entries. For each entry, check if it's a list of exactly two elements. If not, error.
- Check that each key is a string and not empty. Also, check that all keys are unique. If any key is repeated, error.

Once the input is validated, then process each pair. For each key and value, escape backslashes, equals, and semicolons. Wait, the problem says to escape every backslash, equals, and semicolon that occurs inside a key or a value. So, when we process each key and value, we need to escape those characters.

So, for each key and value, we need to replace any occurrence of \, =, ; with a backslash followed by the character. For example, if a key is "a=b", then it should become "a\\=b". Similarly for values.

But how to do that? Maybe create a function that takes a string and escapes those characters. Let's think: for a given string, replace each occurrence of \, =, ; with \ followed by the character. So, for each character in the string, if it is one of those three, we add a backslash before it.

So, the escaping function could be something like:

def escape_special(s):
    return re.sub(r'\\|=*|;', r'\\$\1', s)

Wait, but using regular expressions here. Wait, but maybe using a simple loop. Alternatively, using a regex to replace each occurrence of any of those characters with a backslash followed by the character.

Wait, but the problem says to escape every occurrence. So, for example, if the string is "a=;b", then each = and ; would be escaped. So, the escaped string would be "a\\=;\\;b".

So, the function to escape would be: for each character in the string, if it is \, =, or ;, then replace it with \ followed by the character. So, for each occurrence of those characters, we need to add a backslash before them.

So, perhaps using a regular expression to find all occurrences of those characters and replace them with two characters: a backslash followed by the original.

But how to do that? Let's think. The regex pattern would be [\\=;], which matches any of those characters. Then, for each match, we replace it with \ followed by the original character. So, in Python, using re.sub with a lambda function.

Wait, but in Python, the regex would be r'\\|=*|;' — but that's not correct. Wait, the correct regex would be r'[\=\;\\]' — but in a regex, the backslash needs to