I remember when I first had to learn Access. I was a PC Specialist not a Database Administrator, but I picked it up pretty quick because Access was easy to learn and used GUI for designing forms, reports, queries, etc. Much easier than DBase. The users found it easier because I could put GUI on the forms, and use drop-down combo boxes to select things and populate those combo boxes from a table. No more typos, just select the combo box. Access reports could easily be exported to RTF or Word format and emailed. I even learned how to use MAPI to send out email when something needed attention. But I was also a Developer, learned to program in High School and College, so I picked up Visual BASIC for Applications really fast, being a VB programmer already. Back then it was just called Access BASIC.
Most databases can be imported to Access really easily. Dbase and Clipper use DBF files, which Access can import. Access can read Excel and Lotus spreadsheets too. You can even use ODBC to connect to just about any Windows based Database and link the table and write a simple Append Query to copy the data into an Access table, and then delete the linked table when you are done. The only problem I can see is if it is a custom written Database and not a commercial one. I doubt they would be doing that, it requires a lot of money to support such a database from the company that wrote it, or having developers on staff that can support it. If they have developers on staff to support it, they can export the data for you into a text file, which Access can read and import into a table. Most databases have an export option to export into a text file. So all you really need to learn on the other databases is how to export the data. Just ask for a reference manual and look up the chapter on exporting and importing. See if it can be exported to a file that Access can work with.
For Database Administration work, $7 an hour is very low. Ask her how often you have to import tables and do other Database Administration work. It might just be to get the new database off the ground and get the data imported from the old one. Or maybe once a week to get the data from other campuses and merge it into the main database.
If I was allowed to go back to work, I might take the job myself. I know I can handle it given my extensive background in Access. The only tricky part would be to make the daily quota of Data Entry records, that would be stressful for me too. I know I could teach you enough about Access to get the job done.