Sorry about that, forgot you can use the dot notation with Tasks.  I created this in a dev environment that I have and it should work for you.  You need to gather up all of the accounts before you enter the for loop and make a map out of them.  once you have that, you can apply your logic.

trigger accountTask_Rating on Task (before insert) {
	List<Task> acctTaskList = new List<Task>();
	List<ID> acctIDList = new List<Id>();
	//Loop through the tasks in the trigger and get a list of all the ones that are attached to accounts
	//also create a list of IDs so we can query for the accounts
	for(Task t : trigger.new){
		System.debug('t.whatid is: '+t.whatid);
		if(t.whatid!= null && String.valueOf(t.whatid).startswith('001')){
			acctTaskList.add(t);
			acctIDList.add(t.whatid);
			System.debug('Added Account' + t.whatid);
		}		
	}
	
	//using the list of IDs created above, query for the account information
	List<Account> acctList = [select Id, Rating__c from Account where id IN :acctIDList];
	
	//create a map of the accounts returned in the query
	Map<Id,Account>acctMap = new Map<Id,Account>();
	for(Account a : acctList){
		acctMap.put(a.id, a);
	}
	
	//we now have what we need to process the tasks, 
	for (Task tsk : acctTaskList){			
		//get the account rating from the map and set it to uppercase
		String strRating = acctMap.get(tsk.whatId).Rating__c.toUpperCase();			                                       

		//set budget via Account rating
		if (strRating == 'A1' || strRating == 'A2') {
			tsk.Budget__c = 500;
		} else  if (strRating == 'A3' || strRating == 'A4') {
			tsk.Budget__c = 200;		
		} else  if (strRating == 'A5') {
			tsk.Budget__c = 100;                                        
		} else {
			tsk.Budget__c = 0;
		}                 	
	}			
}