I just did it with about 150 records and imported via a web-based "PHP MyAdmin" on the remote server....just open database in Access, right-click on the table you want to export and choose "export..."
Then make sure you choose to export as a text file (in the pulldown options) and add the extension ".csv" to the filename before exporting. A dialog box will then pop up to let you choose your specific text-file options for exporting.
Once your finished exporting, change the exported .csv file extension to .txt.
Now go to your PHP MyAdmin interface on your web host. If you haven't already, make a table with the same number of columns and the correct data types. Make sure they are in the same order as your exported Access database. Then open the open that table administration page. About half way down the page you'll find the option to "insert textfiles into table". The rest is self explanatory. Worked like a charm for me. I did notice some "#" characters in some of my text fields when viewing from the MyAdmin interface, but when viewed through the actual PHP page the formatting was all intact.
Another hint - open your text file before you import into MySQL and see if just the text fields have quotes around them or if both text and numeric data are within quotes. If just the text is within quotes then make sure to check the option for that on the MyAdmin import screen. Also make sure you set the field delimiters to be commas when importing, or if you used a different delimiter, just make sure you specify that when importing. If you don't understand what I mean, just go try it and you should be able to figure it out.