Jason,
Larry makes some valid points about whether you really wish to delete, as opposed to "de-activate" these records.
Keep this in mind.
Notwithstanding this, it sounds like you have "referencial integrity" set between (some of) the tables in your database. Suggest you read up about this in the online help. Basically it prevents you from deleting records in one table, if related records exist in another (eg. if you have a table called tblInvoices, and another called tblInvoiceLineItems, then it will prevent you from deleting an Invoice header record as long as related record(s) exist of associated Invoice Line items.
To check up on this and remove the RI, or set up "cascading deletions", do the following:
(a) From the database window, right click, and select the Relationships option.
(b) This should display any relationships that have been set up between the tables in the database. If the screen is blank, try selecting the Relationships, Show All options"
(c) The table from which you are trying to delete records from, is probably connected via a relationship line, to one or more other tables. For each of these relationship lines:
(d) Double click on it. I would anticipate that the "Enforce Referencial Integrity" option is set on at least one of these relationships. Where this is the case, toggle on the "Cascade Delete Related Records" option.
(e) Do the above step for each table which is related to the table from which you are attempting to delete the records from.
When this is done, Save and exit the relationships screen. Your delete button should now work, but bear in mind that it will be deleting any associated "child" records as well as the parent record. You may get a warning message about this depending on your option settings.
With all of this, I'm assuming that your tables are held in the same database as the Form that you are working on. If not, you will have to identify the database in which the tables are held, and perform the Relationship changes described above in this database.
Good luck,
Steve