That client is very much out of date, grab it from the EZ4 section of the site:
http://ezflash.sosuke.com/viewtopic.php?f=...793&start=0
(there are two files: a patch update and a client pack. Nothing new has happened in GBA world for about 2 years now so you can ignore the update if you want).
In the 7zip file from the link above there will be a file called
ezfla_up.bin
Add this to the root of the memory card and old R when booting up.
This will update the loader (the one included in the download goes by the name of modulo's RESET loader if you do any more reading and is currently the best loader).
Getting roms onto the card.
Along with that download is a program called EZ4_Client
Run it and the rest should be fairly self explanatory: click open and select what you want to send (they can be in zip/rar format if you like) and press send. Wait for it to finish and you can put the card back in the EZ4 and into your DS.
You can either load the GBA loader from the menu (it will be auto selected in GBA hardware) or use the nopass function/let flashme run it to get the DS loader (both work fine but the DS one is nominally faster and has touchscreen support)
GBA naming list: GBA roms have a fairly unique header so you can make a list and assign names to the roms on it. My list is for the pure rom set but nothing really messes with the headers (some really old dumps that were later nuked had bad headers but you would be hard pressed to find them).
My list is from February so some of the latest roms will not have names and will be send to the cart as .gba. I suggest adding them one by one if you want them (and they are largely region dupes and shovelware) and adding a name to the box in the top left corner. I will update the list at some point in the not too distant future (probably when another update comes).
And yes if you only want GBA you do not need a DS naming list (although the same add it to the top left box thing applies if the list is out of date).
Sidenote on GBA naming: there is a bug in the loader that means some games (mario games are the big one) need to use 8:3 naming (8 characters or less and the extension .gba). On the occasion a game does not save simply rename the game and the save with an 8:3 name (the bug is with loading the save so you should still have the save you made). If I remember I will 8:3 the problem games in the next names list update.
GBA roms are trimmed automatically by EZ4Client.
Your second option is to use rudolph's tools and store the GBA roms on your R4. I am not sure about this one having never done it but it is the same as the 3 in 1 for which there are many threads.
Other tools:
GBATA it is able to patch, trim, IPS patch and much more. Have it for the one or two occasions GBA roms do not patch properly with EZ4 Client.
http://gbadat.altervista.org/datset.htm
Trolleydave also added patching to one of his tools so that may be worth a look.