If you can see the light flash on the keyless entry keypad outside your garage then the issue is not likely to be a battery. Typically the lights flash like that when trying to synchronized signals during programming. In other words, you have a programming related issue.
A couple of things might be happening. First, the universal remote you purchased might not be compatible. Sometimes when that happens it is still possible to program in the incompatible remote but it essentially "locks" the opener programming so that no other transmitters, such as your keyless entry, can then be programmed after it.
Try erasing the memory on the opener using the information in the link below or your manual. Then reprogram in your keyless entry before anything else. If the keyless entry now programs properly the issue was that your replacement remote was incompatible or damaged.
Double-check that you have the complete model number from your opener, if, for example, you have a 139.53985D instead of a 139.53985 the remotes for the two are not compatible. I would suggest you get the correct remote for your model number and not a universal to avoid a repeat of this problem. If you do have a 139.53985 then the remote should be part number 09.009. 53680. If your model number is incorrect here, use the full number and the link below to find the correct remote at the Sears Parts site.
If erasing the memory does not allow you to program in the keyless entry by itself then the keyless entry will need to be replaced. Again, the part information for that will be at the Sears Parts site.