Here's what's up:
The opening <form> tags shouldn't be inside of the table. You can use a table to arrange the form, but you should open the form, then table tags, then close them, and then close the form.
Also, table structure is like this:
<table>
<tr>
<td></td>
</tr>
</table>
This just makes a one-cell table, but that's enough to demonstrate. Each <table> tag *must* have at least one subtag <tr>, and each <tr> *must* have at least one <td> tag.
<tr> defines a table row, whereas <td> defines a cell in a row, without both, you have an empty table.
Looking at what you have there, line by line:
<table> (Opened table, ok)
<tr width="5%"><img src="acmeform,gif"></tr> (Created a row, but you forgot to include <td></td> tags around your image.)
<table> (Opened a second table, you need to put <td> tags AROUND this table as well, since it is inside a cell of the first table.)
<form> (Shouldn't have an opening form tag inside of a table, there's no problems with putting this outside, though. See finished example at the end.)
<td>Full Name: </td> (These <td> tags are not inside of a row, and so this won't display properly.)
<td><input type="text" name="FirstName"/></td>
</tr> (You're closing a table row, but if you count the number of rows you've opened, there is nothing to match this with. You have to balance them, each time you open one, you have to close it.)
</table> (Closed table, ok.)
</form> (Closed Form. You've closed one table, and one form, but you open two tables. You have to close both tables, before closing the form.)
I believe this is what you were going for:
<form>
<table>
<tr width="5%"><td><img src="acmeform,gif"></td></tr>
<tr>
<td>
<table>
<tr>
<td>Full Name: </td>
<td><input type="text" name="FirstName" /></td>
</tr>
</table>
</td>
</tr>
</table>
</form>