What operating system?
Was the database on the old server named 'moodlenew' or did you change the name of the directory from 'moodle' to 'moodlenew' manually? Did you do that with mysqld service running?
When you acquired the raw db directory/files for moodle on crashed server was the mysqld service running? Try to re-acquire the db files with service stopped.
If you have changed the name of directory manually, stop the mysqld service. Then make the directory name match what you see in config.php file of moodle code. Also check ownerships/permissions on not only the directory you renamed, but all files recursively.
Do you know how the moodle crashed? Was the crash originally a DB error?
On the old server, moodle may not work, but what of mysqldump or
phpmyadmin (from which you could get an sql dump)?
Never having been in your situation, the following is google'd research.
https://www.google.com/search?q=Table+doesn%27t+exist+in+engine
Several links ... stackoverflow, dba.stackexchage, etc.
From what I gather of advice in links below, the MySQL server should be stopped
before working with raw database files transfers. So on the 'crashed' server,
stop the mysqld service, Then get a tar ball of your moodle DB directory.
The following from a Linux server running
Server version: 5.7.23 MySQL Community Server (GPL)
[root@sos mysql]# ll
total 221608
-rw-rw----. 1 mysql mysql 56 Mar 23 2017 auto.cnf
-rw-r-----. 1 mysql mysql 26454 Jul 28 10:52 ib_buffer_pool
-rw-rw----. 1 mysql mysql 79691776 Jul 30 05:46 ibdata1
-rw-r-----. 1 mysql mysql 67108864 Jul 30 05:46 ib_logfile0
-rw-r-----. 1 mysql mysql 67108864 Jul 29 01:10 ib_logfile1
-rw-r-----. 1 mysql mysql 12582912 Jul 30 05:46 ibtmp1
drwx------. 2 mysql mysql 32768 May 23 13:06 moodle
drwx------. 2 mysql mysql 4096 Jul 28 11:13 mysql
drwxr-x---. 2 mysql mysql 8192 Jun 8 14:34 performance_schema
drwxr-x---. 2 mysql mysql 8192 Apr 30 13:14 sys
Note the ownerships/permissions on the 'moodle' directory which contains all the raw files for the moodle DB.
On the crashed server, there should also be a config file ... linux typically
found in /etc/ and called my.cnf ... that's a text file and can be edited.
Acqure that file as well.
https://dba.stackexchange.com/questions/111629/table-doesnt-exist-in-engine-after-moving-tables-from-one-vps-to-another
https://stackoverflow.com/a/11506495/2364405
Know this is painful, but please answer the questions at the top.
'spirit of sharing', Ken