How to Recover My database From Old WampServer?
Before I start, I will say that I am not familiar with wampserver but I am familiar with MySQL and LAMP.

First things first, are your tables within your databases MyISAM, InnoDB or a mixture of both? - You can tell on the file level by looking at the suffixes.

MyISAM tables have the table name with the following suffixes:


.frm 
.MYD
.MYI


InnoDB tables have the table name with the following suffixes:


.frm
.ibd


If they are MyISAM, copy the tables straight into the new MySQL database directory and this will work as long as the files have the correct read write permissions and ownership (mysql).

If you have InnoDB tables then this will be an issue because you can't simply copy them into a location, in this case what you would have wanted to do is:


MySQL dump the databases, then MySQL import 
Convert them to MyISAM across the board, make a  copy of the file system, then move them into the new database directory, then change back to InnoDB if needed.


** Please note, do not copy the mysql db if you have it within your backup into the new MySQL directory because this will cause all sorts of issues.